Answer:
x > -3
Step-by-step explanation:
Any negative number greater than -3 will have an absolute value greater than 3.
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
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Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
At the gas station, each liter of gas costs $3 but there's a promotion that for every beverage you purchase you save $0.20 on gas.
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
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Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
In the context of the Pearson r correlation coefficient, the absolute size of r is the:_____.
a. coefficient that indicates the measurement scale that applies to two variables.
b. direction of the relationship between two variables.
c. strength of the relationship between two variables.
d. curvilinear relationship between two variables.
Answer:
strength of the relationship between two variables.
Step-by-step explanation:
The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.
The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.
There are 84 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 3/7 of the remaining students gave their speeches. How many students still haven't given their speeches?
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
Number of students who gave their speech yesterday:-
[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]
so 21 students gave their speech yesterday
remaining students = 84 - 21= 63
Number of students who gave their speech today:-
[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]
Number of students who have given their speech:-
= 21 + 27
= 48
Number of students who still haven't given their speech :-
= total - 48
= 84 - 48
= 36
What is the product? (–3s + 2t)(4s – t)
Answer:
[tex] - 12 {s}^{2} + 11st - 2 {t}^{2}[/tex]Step-by-step explanation:
(–3s + 2t)(4s – t)
= -3s (4s - t) + 2t(4s - t)
[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]
[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]
Answer: -12s^2 + 11st -2t^2
Step-by-step explanation:
= (-3s + 2t)(4s - t)
= -12s^2 + 3st + 8st -2t^2
= -12s^2 + 11st -2t^2
Answer Provided by GauthMath please heart and comment thanks if you like.
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
please help me with this question.
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
Whoever gets this problem right with proper work shown will get brainliest
Answer:
100 % or 1
Step-by-step explanation:
There are two dice
Each dice has a possible roll of 1,2,3,4,5,6
The possible sums are 2,3,4,5,6,7,8,9,10,11,12
The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
Anyone willing to help on this worksheet?
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
Please help me thank you!!!
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation:
write your answer in simplest radical form
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
The line parallel to y = -3x + 4 that passes through (9,-6)
Answer:
y=−3x+21
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
A particular fruit's weights are normally distributed, with a mean of 344 grams and a standard deviation of 10 grams. If you pick 10 fruit at random, what is the probability that their mean weight will be between 334 grams and 354 grams
Answer:
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
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 establishes 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 344 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 344, \sigma = 10[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{10}{\sqrt{10}}[/tex]
What is the probability that their mean weight will be between 334 grams and 354 grams?
This is the p-value of Z when X = 354 subtracted by the p-value of Z when X = 334.
X = 354
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{354 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
X = 334
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{334 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = -3.16[/tex]
[tex]Z = -3.16[/tex] has a p-value of 0.0008.
0.9992 - 0.0008 = 0.9984
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
it takes engineer 3 hrs to drive to his brother's house at an average of 50 miles per hour. if he takes same route home, but his average speed of 60 miles per hour, what is the time, in hours, that it takes him to drive home?
Answer:
t2 = 2.5 hours.
Step-by-step explanation:
The distance is the same.
d = r * t
The rates and times are different so
t1 = 3 hours
t2 = X
r1 = 50 mph
r2 = 60 mph
r1 * t1 = r2*t2
50 * 3 = 60 * t2
150 = 60 * t2
150 / 60 = t2
t2 = 2.5
Answer:
Answer: Travel Time is 2 hours & 30 minutes
Step-by-step explanation:
Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles
Original Distance is 150 miles, New Speed is 60 mph.
Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph
describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point
Answer:
Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.
D
6
5
F
5.5
к.
6.6
What additional information must be known to prove the triangles similar by SSS?
A) No additional information is needed.
B) 2D = LJ
C) The lengths of DG and JL
D) .F.LK
Answer:
C) the length of DG and JL
You start savings a $250 a month for the next 22 years to give us a gift to your daughter when she graduates college if you put the money into a long-term savings account that receives 3.5 interest how much money will you be able to give your daughter
Answer:
$376,475.71
Step-by-step explanation:
FVA Due = P * [(1 + r)n – 1] * (1 + r) / r
FVA Due = 250 * [(1.2916)264 – 1] * (1.2916) / .2916
Are the two figures similar? if they are, solve for the missing side.
Answer:
They are not similar.
Step-by-step explanation:
26 / 13 = 2
24 / 11 = 2.18
They are not proportional which means that they don't have a scale factor and cannot be answered.
1. Prove the following identity:
—> sin^2 theta (1+ 1/tan^2 theta) =1
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Explanation:
[tex]\sin^2(\theta)\times\left(1+\dfrac{1}{\tan^2(\theta)}\right)=\\\\\sin^2(\theta)\times\left(1+\dfrac{\cos^2(\theta)}{\sin^2(\theta)}\right)=\\\\\dfrac{\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta))}{\sin^2(\theta)}=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}[/tex]
The function ƒ(x) = x−−√3 is translated 3 units in the negative y-direction and 8 units in the negative x- direction. Select the correct equation for the resulting function.
Answer:
[tex]f(x)=\sqrt[3]{x}[/tex] [tex]3~units\: down[/tex]
[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]
[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]
----------------------------
Hope it helps..
Have a great day!!
Answer:
its not B that what i put and i missed it
Step-by-step explanation:
Line segment TV is a midsegment of ∆QRS. What is the value of n in the triangle pictured?
A: 6.5
B: 7.6
C: 15.2
D: 3.2
Answer:
D. 3.2
Step-by-step explanation:
Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.
Based on this theorem, we have: TV = ½(RS)
TV = 3n - 2
RS = n + 12
Substitute
3n - 2 = ½(n + 12)
Multiply both sides by 2
2(3n - 2) = (n + 12)
6n - 4 = n + 12
Collect like terms
6n - n = 4 + 12
5n = 16
Divide both sides by 5
5n/5 = 16/5
n = 3.2
