Answer:
1because the occasion of cases
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
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 35113511 grams and a variance of 253,009253,009. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 46174617 grams. Round your answer to four decimal places.
Answer:
The answer is "0.1397".
Step-by-step explanation:
[tex]\mu=3511\\\\[/tex]
variance [tex]\ S^2= 253,009\\\\[/tex]
standard deviation [tex]\sigma =\sqrt{253,009}=503\\\\[/tex]
Finding the probability in which the weight will be less than [tex]4617 \ grams\\\\[/tex]
[tex]P(X<4617)=p[z<\frac{4617-3511}{503}]\\\\[/tex]
[tex]=p[z<\frac{1106}{503}]\\\\=p[z< 2.198]\\\\= .013975\approx 0.1397[/tex]
What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
Find the expression that is equivalent to 7(x2 – 5x + 1).
Answer:
7x^2 -35x +7
Step-by-step explanation:
7(x^2 – 5x + 1)
Distribute
7x^2 -7*5x +7*1
7x^2 -35x +7
A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?
Answer:
13/16 miles per minute
Step-by-step explanation:
Take the miles and divide by the minutes
1/8 ÷ 2/13
Copy dot flip
1/8 * 13/2
13/16 miles per minute
The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash?
Answer:
Hence the probability that she paid cash is 0.105
Step-by-step explanation:
P(cash) = 0.3
P(credit card ) = 0.3
P(debit card ) = 0.4
P ( more than $50 | cash ) = 0.2
P (more than $50 | credit card ) =0.9
P (more than $ 50 |debit card ) = 0.6
P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )
= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4
= 0.57
P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)
= 0.2* 0.3 / 0.57
= 0.105
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
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Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Use a table of values to graph the function ƒ(x) = x−−√. Choose the correct graph from the options below.
Answer:
B
Step-by-step explanation:
The square root function's graph is graph (b). This makes logical sense, because, when taking the square root (the principal root in particular), a general rule is that both the input and the output must be positive. Moreover, if one were to create a table of values to find points on the graph of the function, each of the points can be found on graph (b).
[tex]f(x)=\sqrt{x}[/tex]
x y
1 1
4 2
9 3
16 4
Therefore graph (B) is the correct answer.
Which of the following expressions are equivalent to -3x- 6/10
Choose all that apply:
A=3/6x1/10
b=- 3/10x-6
c= none of the above
Answer:
c= none of the above
Step-by-step explanation:
-3x- 6/10
This has two separate terms, a term with a variable
-3x and a term with a constant -6/10
A=3/6x1/10 This has only one term
b=- 3/10x-6 This has a different x term -3/10 which is not -3
c= none of the above
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation:
A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.
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Answer:
C. h ≥ 1.9 in
Step-by-step explanation:
As the final step, divide both sides of the inequality by 5.3:
(5.3h)/5.3 ≥ 10/5.3
h ≥ 1.9
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.
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
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Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with % confidence if (a) she uses a previous estimate of ? (b) she does not use any prior estimates?
Answer:
732 samples ;
752 samples
Step-by-step explanation:
Given :
α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42
Using the relation :
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.58 * 0.42) / 0.03²
n = 0.65918769 / 0.0009
n = 732.43076
n = 732 samples
B.)
If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.5 * 0.5) / 0.03²
n = 0.67650625 / 0.0009
n = 751.67361
n = 752 samples
someone find x for me lol
Hi there!
[tex]\large\boxed{x = 60^o}[/tex]
We know:
∠AGB ≅ ∠DGC because they are vertical angles. They both are 90°.
∠AGE ≅ FGC because they are vertical angles, equal 30°.
∠BGF ≅ ∠DGE are vertical angles, both equal x.
All angles sum up to 360°, so:
360° = 90° + 90° + 30° + 30° + x + x
Simplify:
360° = 240° + 2x
Subtract:
120° = 2x
x = 60°
^please answer, thanks in advance ^
Answer:
There is not enough information to determine the mean, the median is 28.
There is not enough information to determine the mean absolute deviation, the interquartile range is 18
Step-by-step explanation:
The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.
From the box plot given, the marked point in between the box is 28 cm
Hence, Median = 28 cm
The mean cannot be inferred from the skewed box plot.
There is also not enough information to determine the mean absolute deviation ;
The interquartile range:
(Q3 - Q1)
Q3 = upper quartile, the endpoint of the box = 40
Q1 = the starting point of the box = 22
IQR = Q3 - Q1
IQR = 40 - 22 = 18
13 A traffic roundabout has a circular garden
in the centre and two lanes for traffic
encircling the garden. The diameter of the
garden is 16 metres and each lane is 3 metres
wide. Each lane is to be resurfaced. Calculate
the area to be resurfaced. Answer in square
metres to the nearest whole number.
Answer:
Step-by-step explanation:
The area to be resurfaced is the area of the
whole circle including garden and lanes minus
the area of the garden.
Area of a circle is (pi)r2
radius of garden is (1/2)diameter = 8 m
Garden area: (pi)82 = 64(pi) m2
Diameter of garden plus traffic lanes is
16 + 2(6) because we add 6 m to both sides
of the diameter of the garden.
Full diameter = 16+12 = 28 m
Full radius = 28/2 = 14 m
Full area: (pi)142 = 196(pi) m2
Area to be resurfaced:
196(pi) - 64(pi) = 132(pi) m2 ≅ 415 m2
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
Can someone explain how to solve this step by step? Thank you
Answer:
x=10
Step-by-step explanation:
Using the Rational Roots Test, we can say that the potential rational roots are
± (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
Unfortunately, there doesn't really seem to be an easy way to figure out which numbers are actually roots outside of guess and check. Therefore, to solve this, we'll have to go through numbers until we hit something.
To make the process faster, I wrote a Python script as follows:
numbers = [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
negative_numbers = [i * (-1) for i in numbers]
numbers = numbers + negative_numbers
for i in numbers:
if (i**3 - 10*(i**2) + 9*i-90) == 0:
print(i)
The result comes out as 10, meaning that 10 is our only rational root. Using the Factor Theorem, we can say that because 10 is a root, (x-10) is a factor of the polynomial. Using synthetic division, we can divide (x-10) from the polynomial to get
10 | 1 -10 9 -90
| 10 0 90
_________________
1 0 9 0
Therefore, we can say that
(x³-10x²+9x-90)/(x-10) = (x²+0x+9), so
x³-10x²+9x-90 = (x-10)(x²+9)
As the only solution to x²+9=0 contains imaginary numbers, x=10 is the only solution to x³-10x²+9x-90 = (x-10)(x²+9) = 0
please help me its timed -H.M
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
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
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
What is the value of Z? Z =2^3
the value of Zis 8.
Z =2^3=8
Now we have to,
find the required value of Z.
→ Z = 2^3
→ [Z = 8]
Therefore, value of Z is 8.
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
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.
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
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
Find the number that comes after 144five
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
