[tex]range=524.[/tex]
Step-by-step explanation:
[tex]range \: is : max - min \\ the \: range \: is \: : 529 - 5 = 524. \\ regards \\ ♨Rage♨[/tex]
The range of the given data set comes to be 524.
The given data set is: 52, 24, 5, 72, 49, 529
What is the range of a data set?The range of a data set is the difference between the maximum and minimum value of that data set.
The maximum value of the given data set = 529
The minimum value of the given data set = 5
The difference between the maximum and minimum value of that data set=529-5 =524
So, the range of the data set =524
Therefore, the range of the given data set comes to be 524.
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MULTIPLE CHOICE CALCULUS
1) An object moves along a line so that its position at time t is s(t) = t^4 - 6t^3 - 2t - 1.
At what time t is the acceleration of the object zero?
A. at 3 only
B. at 0 and 3 only
C. at 0 only
D. at 1 only
2) If f(x) = e^x (sin x + cos x), then f'(x) =
A. 2e^x (cos x + sin x)
B. e^x cos x
C. e^x (cos^2x - sin^2x)
D. 2e^x cos x
Answer:
1) B. at 0 and 3 only
2) D. 2eˣcosx
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringQuadraticsCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sinu] = u'cosu[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[cosu] = -u'sinu[/tex]
eˣ Derivative: [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]
Step-by-step explanation:
*Note:
Velocity is the derivative of position.
Acceleration is the derivative of velocity.
Question 1
Step 1: Define
s(t) = t⁴ - 6t³ - 2t - 1
Step 2: Differentiate
[Velocity] Basic Power Rule: s'(t) = 4 · t⁴⁻¹ - 3 · 6t³⁻¹ - 1 · 2t¹⁻¹[Velocity] Simplify: v(t) = 4t³ - 18t² - 2[Acceleration] Basic Power Rule: v'(t) = 3 · 4t³⁻¹ - 2 · 18t²⁻¹[Acceleration] Simplify: a(t) = 12t² - 36tStep 3: Solve
[Acceleration] Set up: 12t² - 36t = 0[Time] Factor: 12t(t - 3) = 0[Time] Identify: t = 0, 3Question 2
Step 1: Define
f(x) = eˣ(sinx + cosx)
Step 2: Differentiate
[Derivative] Product Rule: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x\frac{d}{dx}[sinx + cosx][/tex][Derivative] Rewrite [Derivative Property - Addition]: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] eˣ Derivative: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] Trig Derivatives: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(cosx - sinx)[/tex][Derivative] Factor: [tex]\displaystyle f'(x) = e^x[(sinx + cosx) + (cosx - sinx)][/tex][Derivative] Combine like terms: [tex]\displaystyle f'(x) = e^x[2cosx][/tex][Derivative] Multiply: [tex]\displaystyle f'(x) = 2e^xcosx[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
SOLVE FOR X PLEASE
10x+50+80=180
Answer:
x= 5
Step-by-step explanation:
10(5)+50+80=180
Multiply the 5 by 10
10*5=50
50+50+80=180
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x=5
Step-by-step explanation:
10x+50+80=180
combine 10x(50+80)=180, 10x+130=180
subtract 10x(130-130)=(180-130), 10x=50
divide 10 by 50 to find x=5
hope the step by step helps
Marta walked at 4.7 miles per hour for 0.71 hours. How far did she walk?
Answer:
3.337 miles
Step-by-step explanation:
D = Distance
S = Speed
T = Time
D = S x T
D = 4.4 x 0.17
D = 3.337
this is a kind weird number so this might be wrong tho
5.35
2.2 Show your work please!
Answer:
what lesson in math is this??
There are 7 times as many dogs as cats. If the total number of dogs and cats is 32, how many dogs are there?
Evaluate the line integral, where C is the given curve. (x 6y) dx x2 dy, C C consists of line segments from (0, 0) to (6, 1) and from (6, 1) to (7, 0)
Answer:
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
Step-by-step explanation:
The integral of the curve is given as:
[tex]\int (x +6y) \ dx +x^2 \ dy[/tex]
Where the line segment from (0,0) to (6,1) is:
0 < x < 6 and [tex]y = \dfrac{x}{6} \implies dy = \dfrac{dx}{6}[/tex]
Thus;
[tex]\int ^{6,1}_{0,0} (x+ 6 * \dfrac{x}{6}) \ dx + \dfrac{x^2*dx}{6 } = \int^6_0 (x+x+\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \int^6_0 (2x +\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} \dfrac{2x^2}{2}+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} x^2+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} (6)^2+\dfrac{(6)^3}{18} \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} 36+12 \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx =48 --- (1)[/tex]
Similarly; at (6,1) to (7,0)
[tex]\implies 6 \leq x \leq 7 \ and \ y = -x +7[/tex]
Thus; the integral can be computed as :
[tex]\int ^{(7,0)}_{(6,1)} \ (x+6(-x+7)) \ dx + x^2 (-dx) = \int^7_6 (-5x +42 -x^2) \ dx[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5x^2}{2}+ 42x -\dfrac{x^3}{3} \end {bmatrix}^7_6[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(7^2-6^2)}{2}+ 42(7-6) -\dfrac{(7^3-6^3)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(49-36)}{2}+ 42(1) -\dfrac{(343-216)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(13)}{2}+ 42 -\dfrac{(127)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{-195+252-254}{6}\end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= - \dfrac{-197}{6} --- (2)[/tex]
By adding (1) and (2) ; we have:
[tex]\int _c (x+6y)\ dx + x^2 \ dy = 48 + (-\dfrac{197}{6})[/tex]
[tex]\int _c (x+6y)\ dx + x^2 \ dy = (\dfrac{288-197}{6})[/tex]
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
What is the value of the variable z and the measure of Angle B?
Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?
30° only
90° only
30° or 150°
30°, 90°, or 150°
Double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
So rewrite the equation as
sin(2x) = cos(x)
2 sin(x) cos(x) = cos(x)
2 sin(x) cos(x) - cos(x) = 0
cos(x) (2 sin(x) - 1) = 0
There are two cases,
cos(x) = 0 or 2 sin(x) - 1 = 0
cos(x) = 0 or sin(x) = 1/2
In the interval 0º ≤ x < 180º, we have cos(90º) = 0 and sin(30º) = sin(150º) = 1/2, so the possible values are 30º, 90º, or 150º.
Answer:
D. 30°, 90°, or 150°
Step-by-step explanation:
got it right on edge :)
BRAINLIEST!!!
Consider points A(3, 6) and B(8, 4). Find point C on the x-axis so AC +BC is a minimum.
I need help
Answer:
(6,0)
Step-by-step explanation:
Micah drew a picture of a flag on graph paper. He will color the flag red and blue.
What is the area, in square units, of the part of the flag Micah will color red?
pls help!
Answer:
The area of Micah's flag, in square units, would be 44² units.
Kelly received a 35% discount on the purchase of a $320 bicycle. What was the amount of the discount?
$432.00
$208.00
$112.00
$35.00
Answer:
$112
Step-by-step explanation:
$320 X .35= $112
3. The temperature was 8°F. It dropped so that the temperature was 0°F.
Answer:
is this a question?
Step-by-step explanation:
yes it dropped 8°F
What is the greatest common factor of 25 and 45?
Answer:
5
Step-by-step explanation:
Factors of 25: 1, 5, 25Factors of 45: 1, 3, 5, 9, 15, 45The greatest factor that's in both lists is 5.I hope this helps!
The greatest common factor of 25 and 45 is 5.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given numbers are 25 and 45.
To find the greatest common factor, factorize the numbers,
Factor of 25 = 5 × 5
Factor of 45 = 3×3×5
The common term in 5 × 5 and 3×3×5 is 5.
Therefore, the greatest common factor is 5.
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Suppose you roll a special 4-sided die. What is the probability that the number rolled is a "1" OR a "2"?
awnser:25%
because 4/100=25
The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/2
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
You roll a special 4-sided die.
Now, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
And, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
Hence, The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/4 + 1/4
⇒ 2/4
⇒ 1/2
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152 is the product of hectors age and 8
Answer:
If its asking for hectors age, then its 152/8=19
Step-by-step explanation:
Answer:
144
Step-by-step explanation:
152-8
Which of the following relations has a domain of {-4, -2, 1)?
O {(1, 2), (-2, 3), (4, 6)}
O {(1, 2), (-2, 2), (-2, 4), (4, -4)}
O {(1,2), (-2, 2), (-2, 4), (-4,4)}
O None of the other answers are correct
O {(-1, 2), (4,3).(-2, 6), (-2,3)}
Answer:
Third answer option
{(1,2), (-2, 2), (-2, 4), (-4,4)}
Step-by-step explanation:
If the Domain is the set = { -4, -2, 1}, we need a relationship that shows pairs with first coordinates as described below:
(-4, ...) , (-2, ...) and (1, ...)
which we find in the third option shown:
{(1,2), (-2, 2), (-2, 4), (-4,4)}
John has $255 in his bank account. His bank charges a $10.50 administration fee each month. If he makes no other deposits or withdrawals, how much money is in John’s account at the end of 5 months?
Answer:
10.50×5=52.50 255-52.50=202.50
Step-by-step explanation:
well if 10.50 is taken for 5 months he will have 202.50 because 255-52.50=202.50
I need help plz ASP
Answer:
b. 20 songs
Step-by-step explanation:
when you look at (0,0), the y-intercept is 20, so that is the initial starting point.
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.
Answer:
Please answer my questions you'll get points
Answer:
The smaller angle is 39, the other is 51
Step-by-step explanation:
The vegetable display automatically sprays a mist over the vegetables according to a repeating timer you set. How many minutes should you set the timer for in order to spray the vegetables 5 times each hour
Answer:
✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️
You have 1 quarts of brown stock.
You need 1 cups to make one serving of braised short ribs.
How many servings can you make?
(don't include partial portions)
I
Answer:
Answer:
you can make 4 servings because 1 quart is 4 cups
The perimeter of quadrilateral ABCD is 85. Find the value of x.
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
What is meant by Quadrilateral?A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side." A quadrilateral is depicted in the image above. The outcome of an image The perimeter of the quadrilateral ABCD is 85 feet. Find out what the value of x is.The perimeter of a quadrilateral is the entire length of its boundary. Perimeter = AB + BC + CD + DA, for example, can be used to define the perimeter of the quadrilateral ABCD.The perimeter is 85. (the total of all sides). X = 5.5, and 4x + 3x + 4 + 5x-7 + 6x-11 = 85 (18x - 14 = 85). 18 x = 85 + 14 = 99.Therefore,
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
When we substitute the provided values, we get: ABCD perimeter = 9 units plus 5 units plus 9 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units As a result, the perimeter of ABCD is 28 units.
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A glacier in Alaska moves about 29.3 meters a day. About how much farther will it move in 1000 days then it will move in 100 days?
A glacier will move about ______ meters farther in 1000 days then it will move in 100 days.
Fill in the blank
Your answer has to be in decimal form.
BIG THANKS!
Answer:
If it moves 29.3 meters a day, then we need to find the total amount of days:
1000 days + 100 days = 1100 days
Since it moves 29.3m per day, we can write:
29.3m x 1100 which equals 32230m
So it moved 32230 meters
Step-by-step explanation:
What is the result of factoring out the GCF from the expression (24 + 36)?
please i need help!
it is on PLATO
Answer:
I gues answer is 4( factor)
HELPPPPPPPPPPPPPPPPPPPPPPPPPP
Which intervals is this function graph decreasing? Select 2 answers. *
[ -5.5, -5]
[ -5, -4]
[ -3, 1]
[1,2]
Choice B. [-5, -4]
Choice D. [1, 2]
===================================================
Explanation:
We're looking for portions when the graph goes downhill when we move from left to right.
The first portion is from x = -5 to x = -4. So we write [-5, -4] which represents [tex]-5 \le x \le -4[/tex]
The second portion is [1, 2] which goes downhill since the interval starts at x = 1 and stops at x = 2.
The portions are highlighted in the diagram below.
As you can see, we only care about the x values for any given interval. The y values don't matter as long as they decrease along the interval.
What is the slope of the line in the graph below? Show your work. PLEASE HELP PLEASE
Answer:
5/2
Step-by-step explanation:
The line crosses two points: (0,1) and (5,3)
You can then use the slope-point formula to find the slope:
(x1 - x2)/(y1 - y2) =
(0 - 5)/(1 - 3) =
-5/-2 =
5/2
Answer:
The slope of the line is 2/5
Step-by-step explanation:
Start counting where the y-intercept is. The y-intercept is at (0,1). The line is positive since it is increasing from left to right, so you need to count up and then to the right in order to find the slope. You need to find a point where the line intercepts a coordinate point directly on the line. If you look at the point (5,3) it is directly on the intersection that runs up and down. Start at 1 and count 2 up and 5 to the right. You will end up on the point (5,3). Hope this helps. Ask more questions if you need to
Xavier saved money to purchase a bike that originally cost $250, not including tax. The store discounted the bike by 20%. What is the discounted price he will pay for the bike, not including tax?
Question 1 options:
$50.00
$300.00
$270.00
$200.00
HELP I WILL GIVE BRAINLIEST
A classroom of children has 17 boys and 19 girls in which five students are chosen to do presentations. In how many ways can the five students be chosen so that more boys than girls are selected
Answer:
167688 ways
Step-by-step explanation:
Given that:
Number of boys = 17 &;
Number of girls = 19
The number of ways that five students can be chosen such that more boys than girls are selected are:
The ways of choosing = 5 boys 0 girls + 4 boys 1 girl + 3 boys 2 girls
The ways of choosing = [tex]^{17}C_5 +( ^{17}C_4 \times ^{19}C_1} )+( ^{17}C_3 + ^{19}C_2})[/tex]
The ways of choosing = [tex]\dfrac{17!}{5!(17-5)!} + \begin {pmatrix} \dfrac{17!}{4!(17-4)!} \times \dfrac{19!}{1!(19-1)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(17-3)!} \times \dfrac{19!}{2!(19-2)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17!}{5!(12)!} + \begin {pmatrix} \dfrac{17!}{4!(13)!} \times \dfrac{19!}{1!(18)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(14)!} \times \dfrac{19!}{2!(17)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17*16*15*14*13*12!}{5!(12)!} + ( \dfrac{17*16*15*14*13!}{4!(13)!} \times \dfrac{19*18!}{1!(18)!} ) + ( \dfrac{17*16*15*14!}{3!(14)!} \times \dfrac{19*18*17!}{2!(17)!} )[/tex][tex]=6188 + ( 2380\times19 ) + (680 \times171)[/tex]
= 167688 ways
Using the combination principle, the number of ways of selecting 5 students such that the number of boys is greater the number of girls selected ls 167688 ways.
Number of boys = 17Number of girls = 19Number of selections to be made = 5
In other to choose more boys than girls :
5 boys and 0 girls4 boys and 1 girl3 boys and 2 girlsUsing the combination relation :
(17C5 × 19C0) + (17C4 × 19C1) + (17C3 × 19C2)
(6188 × 1) + (2380 × 19) + (680 × 171)
(6188 + 45220 + 116280)
= 167688 ways
Therefore, the Number of ways of making the selection is 167688 ways
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Need help on this will give brainlist
Answer:
53
Step-by-step explanation:
Alternate interior angles are the same value.
A car is traveling at a constant speed. It travels 34 miles in 5 minutes.
How many minutes will it take the car to travel 70 miles?
helppppp
Answer:
10.30 or 10 1/6 if this answer is not on the answer choices round to the nearest answer close to this.
Step-by-step explanation:
how to solve.
34/5=6.8 - this is how many miles the car is traveling per minuet.
6.8/70=10.30 - this should be the answer because this is how many minutes it takes the car to travel 70 miles
