math hw for tonight
help solve this problem! Thank you!
ap cal bc
The antiderivative of the function is t³/3 i + ln |cos(t)| j.
option C.
What is the antiderivative of the function?The antiderivative of the function is calculated as follows;
r = t²i + tan(t)j
tan(t) = sin(t)/cos(t)
Substituting sin(t)/cos(t) for tan(t) in the given function;
r = t²i + (sin(t)/cos(t))j
The antiderivative of sin(t)/cos(t) with respect to t is calculated as;
u = cos(t)
du = -sin(t)dt
∫ (sin(t)/cos(t)) dt = -∫ du/u
= -ln |u| + C
= -ln |cos(t)| + C
The antiderivative of t² is calculated as;
∫ t² dt = t³/3 + C
Add the two equations, to obtain the antiderivative;
∫ r dt = t³/3 i + ln |cos(t)| j
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The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0.
What is Ø?
The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.
The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).
According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.
Comparing the radial distances;
|r| = 3 (for (3, 45°))
|-r| = 3 (for (-3, Ø))
Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.
Comparing the angles;
θ = 45° (for (3, 45°))
θ = Ø (for (-3, Ø))
Since the angles are equivalent, we can equate them:
45° = Ø
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Asap need help quick
The function rule for the graph is -2 ≤ x ≤ 1 , where x is the domain
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is plotted on the graph
The values of the output represents the range of the function and the domain of the function is the input
So , the x values ranges from [ -2 , 1 ]
Hence , the function rule is domain ranges from -2 ≤ x ≤ 1
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Help time limit
State the domain and range for each graph and then tell if the graph is a function (yes or no)
Answer:yes, it’s a function, domain is all real # range all real #
Step-by-step explanation:
Help I am so confused. Thank you pic at bottom
1A) This sampling technique employed is known as a systematic random sample.
1B) The demographic examined in the study is the total production run of 15,600 LED monitors. The representativeness of the sample within such population is relied upon if every 120th monitor selected is an unbiased, irregular choice from the larger collective.
How to explain the samplingFor question 2, the sampling method utilized here is called a convenience sample. Kenya only enquires the middle school pupils in her 7th grade science course, which cannot be characterized as a representative or randomly chosen group of all middle school learners.
The sample may not accurately reflect the population because it merely involves students in her lesson, and not necessarily those enrolled at her school or district.
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Day 3
June is setting up an experiment involving lima beans. She places a lima
bean inside a damp paper towel, then places it in a baggie. June takes
another lima bean and places it in a dry paper towel and puts it in a
baggie. She puts both baggies on a windowsill next to each other. She
checks each day to observe the changes.
What testable question is June most likely trying to answer?
A. Can lima beans grow in a paper towel?
B. Does the amount of light affect how fast a lima bean grows?
What does a lima bean look like once it is sprouted?
Which sprouts faster, a moist lima bean or a dry lima bean?
On
The testable question can be Which sprouts faster, a moist lima bean or a dry lima bean?
We have,
June laces a lima bean inside a damp paper towel, then places it in a baggie.
June takes another lima bean and places it in a dry paper towel and puts it in a baggie.
The Experiment is related to moisture because one damp and one dry towel is used.
So, the testable question can be
Which sprouts faster, a moist lima bean or a dry lima bean?
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Solve for x 3x + 1 ≤2-x< 18+ 7x
Answer:
X can be any number greater than -2 and less than or equal to 1/4.
Step-by-step explanation:
To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.
3x + 1 ≤ 2 - x
Adding x to both sides, we get:
4x + 1 ≤ 2
Subtracting 1 from both sides, we get:
4x ≤ 1
Dividing both sides by 4, we get:
x ≤ 1/4
Next, we solve the second inequality:
2 - x < 18 + 7x
Adding x to both sides, we get:
2 < 18 + 8x
Subtracting 18 from both sides, we get:
-16 < 8x
Dividing both sides by 8, we get:
-2 < x
Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:
-2 < x ≤ 1/4
This means that x can be any number greater than -2 and less than or equal to 1/4.
Determine the measures of the arcs and angles:
*It may help to find all central angle measures before answering the hotspots.
If you do any calculating, you can type that into the hotspot with your final answer.
m HE
m HD
m DG
m EG
m < DEG
m < HGE
The values of the arc length and angles are:
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
We have,
The central angle is equal to the intercepted arc length.
So,
62° = HE
And,
∠A = HD
∠A + 62 = 180
∠A = 180 - 62
∠A = 118
HD = 118
And,
DG = ∠M (say)
∠A + 118 = 180
∠M = 180 - 118
∠M = 62
DG = 62
And,
∠A is opposite to ∠N (say)
So,
∠A = ∠N = 118
∠A = EG
EG = 118
And,
From the definition of the exterior angle.
∠DEG + ∠HGE = 62 ______(1)
Also,
The sum of the three angles in AEG = 180
∠EAG + ∠DEG + ∠HGE = 180
∠EAG = 180 - 62 = 118
So,
∠DEG + ∠HGE = 180 - 118
∠DEG + ∠HGE = 62 _______(2)
Thus,
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
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Help!!
how many combinations do I have it I select 4 things from a total of 9 without replacement? (9C4)
4 things can be selected from a total of 9 without replacement in 126 times without replacement.
What is Combination?Combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of selection does not matter.
How to determine this
To calculate the combination without replacement
nCr = n!/r!(n-r)!
9C4= 9!/4!(9-4)!
= 9!/4!(5!)
= 9*8*7*6*5*4*3*2*1/4*3*2*1*5*4*3*2*1
= 362880/24*120
= 362880/2880
= 126
Therefore, it can be combined in 126 times
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Determine which function is represented by the graph.
(a) f ( x ) = 4 cos ( x + π )
(b) f ( x ) = 4 cos 4 x
(c) f ( x ) = 4 sin ( x − π )
(d) f ( x ) = − 4 cos ( x + π )
(e) f ( x ) = 1 − sin x /2
Answer:
The graph appears to be a cosine function that has been shifted π units to the left and vertically reflected.
Option (d) represents this transformation:
f(x) = -4 cos(x + π)
Therefore, the answer is (d).
Step-by-step explanation:
Question 2 (1 point) A new car cost $30,000. Each year, it depreciates by an average of 14%. What rule is the explicit rule for the situation?
A. an = 30,000 . 0.14n-1
B. an = 30,000 . 0.86n-1
C. an = 30,000 . 1.14n-1
The explicit rule for the situation whereby a new car that costs $30,000 depreciates at an average rate of 14% per year, giving the depreciated value of the car after n years, is given by B. an = 30,000 × 0.86^n-1.
What is the depreciated value of an asset?The depreciated value of an asset in any year can be determined using the exponential decay function or equation.
An exponential decay equation shows the value of an asset given a constant rate of periodic decrease.
The cost of the new car = $30,000
The average depreciation rate per year = 14%
Depreciation factor = 86% or 0.86 (1 - 14%)
Let the number of years after the purchase = n
Let the depreciated value after n years = an
Decay Equation:an = 30,000 × 0.86^n-1.
Thus, the correct explicit rule is Option B.
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IZ:
eighted Average
Calculator
There are 15 people in a book club. Ten people read for an average of 65 minutes each day. The remaining people read for an average
of 35 minutes each day.
What was the average reading time for the entire book club each day?
Enter your answer in the box.
min
1 2 3 4
5 Next >
Readin
The average reading time for the entire book club each day is 55 minutes
What was the average reading time for the entire book club each day?From the question, we have the following parameters that can be used in our computation:
10 with a weight of 65 minutes5 with a weight of 35 minutesThe weighted average of the numbers is calculated as
Average = Product of numbers and weights/Sum of weights
So, we have
Average = (10 * 65 + 5 * 35)/15
Evaluate
Average = 55
Hence, the weighted average is 55
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Find the value of x
Will mark as brainliest if correct
Provide explanation.
geometry pls helppppp
A graph of triangle ABC is shown below.
A graph of triangle A'B'C, the image of ΔABC after a translation right 1, down 3 is shown below.
A graph of triangle A"B"C", the image of ΔABC after a dilation of 2 is shown below.
ΔA"B"C" does not represent a rigid motion because the pre-image and the image are not congruent.
How to perform the sequence of transformations?By translating the pre-image triangle ABC vertically down 3 units and horizontally right 1 unit, the coordinates of the image of triangle A'B'C'D' include the following:
(x, y) → (x + 1, y - 3)
Coordinate A = (2, 3) → Coordinate A' = (2 + 1, 3 - 3) = (3, 0)
Coordinate B = (4, 0) → Coordinate B' = (4 + 1, 0 - 3) = (5, -3)
Coordinate C = (5, 4) → Coordinate C' = (5 + 1, 4 - 3) = (6, 1)
By applying a dilation with a scale factor of 2 centered at the origin, we have:
Coordinate A = (2, 3) → Coordinate A" = (4, 6)
Coordinate B = (4, 0) → Coordinate B" = (8, 0)
Coordinate C = (5, 4) → Coordinate C" = (10, 8)
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Find the height of the rectangular prism (You should have at least 3 steps shown in your work)
Answer:
[tex]12 \times 10 \times h = 3600[/tex]
[tex]120h = 3600[/tex]
[tex]h = 30[/tex]
The height is 30 millimeters.
Simplify.
^m√a^2m
help asap please
Answer:
Step-by-step explanation:
m
2
−2m−8
Factor the expression by grouping. First, the expression needs to be rewritten as m
2
+am+bm−8. To find a and b, set up a system to be solved.
a+b=−2
ab=1(−8)=−8
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −8.
1,−8
2,−4
Calculate the sum for each pair.
1−8=−7
2−4=−2
The solution is the pair that gives sum −2.
a=−4
b=2
Rewrite m
2
−2m−8 as (m
2
−4m)+(2m−8).
(m
2
−4m)+(2m−8)
Factor out m in the first and 2 in the second group.
m(m−4)+2(m−4)
Factor out common term m−4 by using distributive property.
(m−4)(m+2)
=
Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ =(-6,5), P2 = (5,5)
V=
(Type your answer in terms of i and j.)
The Vector form is v = 11i + 0j.
We have,
P₁ =(-6,5), P2 = (5,5)
If we have the point p1 and p2 then the vector form p1 -> p2 is
v = p2 - p1
v = [ p(2x) - p(1x)) i + [ p (2y) - p(1y)] j
v = (5 - (-6)) i + (5 - 5)j
v = 11i + 0j
v = 11 i
Thus, the vector form is v = 11i + 0j.
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Find the value of each variable. Round your answers to the nearest tenth.
Answer:
k = 8.4; j = 13.1
Step-by-step explanation:
We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio
The tangent ratio is tan(reference angle) = opposite / adjacent, while the cosine ratio is cos(reference angle) = adjacent / hypotenuseIf we allow 40 to be our reference angle...
the measuring j units is the hypotenuse, the side measuring k is the opposite side, and the side measuring 10 is the adjacent side.Because we're not given the measure of either j or k, we have to use 10 each time
Steps to find j:
To find j, we can use the cosine ratio:[tex]cos(40)=\frac{10}{j}\\ \\j*cos(40)=10\\\\j=\frac{10}{cos(40)}\\ \\j=13.05407289\\\\j=13.1[/tex]
Steps to find k:
To find k, we can use the tangent ratio:[tex]tan(40)=\frac{k}{10}\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k[/tex]
I need help
Given the function f(t) = 2t + 1 and its domain is described by the set (1, 2, 3, 5) what is the range? (Enter the values of the range from least to greatest
The range of the given linear function; f(t) = 2t + 1 given its domain (1, 2, 3, 5) is; (3, 5, 7, 11).
What is the range of the given function?It follows from the task content that the range of the given function is to be determined given its domain as defined by the set; (1, 2, 3, 5).
Therefore;
At t = 1; f(1) = 2(1) + 1 = 3.
At t = 2; f(2) = 2(2) + 1 = 5.
At t = 2; f(3) = 2(3) + 1 = 7.
At t = 5; f(5) = 2(5) + 1 = 11.
Ultimately, the range of the given function as required is given by the set; (3, 5, 7, 11).
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Heart attacks cause many deaths. Researchers in the Physicians Health Study (1989) gave a large sample of healthy male physicians either a low dose of aspirin or a placebo.
In this example of heart attack, it would be appropriate to calculate Conditional row percentages. Therefore, the correct option is option A.
When the blood supply for the heart is significantly impeded or blocked, a heart attack happens. The accumulation of fat, cholesterol, and other chemicals in the heart's (coronary) arteries is typically what causes the obstruction. Plaques are the name given to the fatty, cholesterol-containing deposits.
Atherosclerosis is the name for the phenomenon of plaque accumulation. A plaque may occasionally burst and generate a clot that restricts blood flow. A portion for the heart muscle can be harmed or destroyed by a shortage of blood flow. In this example, it would be appropriate to calculate Conditional row percentages.
Therefore, the correct option is option A.
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Your question is incomplete but most probably your full question was,
The constraints of a problem are listed below. What are the vertices of the feasible region?
[tex]x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0[/tex]
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
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If r = 6 and the measure of the central angle 2pi/3, what is the length of the intercepted arc
The length of the intercepted arc is 4π unit.
We have,
Angle = 2π/3 = 2(180)/ 3 = 120 degree
r = 6 unit
So, length of Arc
= θ /360 x 2πr
= 120/360 2 π(6)
= 1/3 (12)π
= 4π unit
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
second option
Step-by-step explanation:
the volume of a cone is calculated as
[tex]\frac{1}{3}[/tex] πr²h
the volume of a sphere is calculated as
[tex]\frac{4}{3}[/tex] πr³
then the volume of a hemisphere is
[tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³
then the volume (V) of the composite solid is
V = [tex]\frac{1}{3}[/tex] πr²h + [tex]\frac{2}{3}[/tex] πr³
Help me with this................
The distribution of the numbers of siblings is best described as skewed to the right so, the median will be a more appropriate measure of the center than the mean
What is positively skewed data?If data is positively skewed - which means that the tail of the distribution leans towards higher values - the median will often be a superior indicator for ascertaining the center than the mean.
This advantage can be attributed to the fact that the median outright ignores extreme values, unlike the median which may become influenced by them and thus pulled towards the extremes of the overall set. Since it is simply the middle value obtained upon sorting the data, its sensitivity to conspicuous outliers is more limited.
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The outcome of spinning 2 spinners 100 times is shown in the table. How many times would you expect these spinners to land on the same number in 10 spins?
We would expect the spinners to land on the same number approximately 2 times in 10 spins.
Based on the given probabilities, we know that the probability of the red spinner and blue spinner landing on the same number is 21%, and the probability of them landing on different numbers is 79%. We can use this information to calculate the expected number of times the spinners would land on the same number in 10 spins.
If we assume that the probability of the spinners landing on the same number is constant across all 10 spins, then we can model the number of times they land on the same number as a binomial distribution with n=10 (number of trials) and p=0.21 (probability of success).
Using the formula for expected value of a binomial distribution, we can calculate the expected number of times the spinners would land on the same number in 10 spins as:
E(X) = np = 100.21 = 2.1
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Complete question is:
The outcome of spinning 2 spinners 100 times is shown as.
Events Actual outcomes Probability
P(red spinner = blue spinner) 21 21%
P(not red spinner = blue spinner) 79 79%
How many times would you expect these spinners to land on the same number in 10 spins?
dillon has a bank account that pays 3.2% simple interest. his balance is $1,766. how long will it take for the amount in the account to grow to $2,000? round to the nearest year.
It will take approximately 4 years for the amount in Dillon's bank account to grow to $2,000.
We use the formula for simple interest to solve this problem;
I = P × r × t
where;
I = the interest earned
P = the initial principal (balance) = $1,766
r = the interest rate (as a decimal) = 3.2% = 0.032
t = the time (in years) we need to find
We know that the interest earned is the difference between the final amount (balance + interest) and the initial principal (balance), so we can write;
Interest = Final Amount - Initial Principal
Plugging in the values, we get;
I = $2,000 - $1,766
I = $234
Now we can substitute the values of I, P, and r into the simple interest formula and solve for t;
234 = 1766 × 0.032 × t
Dividing both sides of the equation by (1766 * 0.032) to isolate t:
t = 234 / (1766 × 0.032)
t ≈ 4.19
So, it will take approximately 4.19 years for the amount in Dillon's bank account to grow to $2,000. Since time cannot be in decimal years, we round to the nearest whole year:
t ≈ 4
Therefore, it will take 4 years for the amount in Dillon's bank account to grow to $2,000.
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I need help on the things in the image
The match of the given words as per the definition of the terms related to data set is as follow.
1 → g
2 →c
3 → b
4 → d
5 → f
6 → a
7 → e
The description of the each word as per the definition is ,
Mean represents the average of the data.
1→g
Spread represents the similarity or variability of the set of observed values of the data.
2→c
Center represents the middle value of the data set.
3→ b
Shape represents the values of the data set when plotted on the graph.
4 → d.
Median represents the middle value of the data set after arranging in ascending or descending order.
5 →f
Distribution represents measure of all the values of the data set spread.
6→a
variability represents the set of such values which satisfies the statistical question or relation.
7 → e.
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HELP ASAP
Find the diameter of the sphere.
Round to the nearest
hundredth.
Rounding to the nearest hundredth, the diameter of the sphere is approximately 4.26 cm.
What is the diameter of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The surface area of a sphere is expressed as:
S = 4πr²
Where S is the surface area and r is the radius of the sphere.
Given that surface area of 18.2π cm²
We can solve for the radius as follows:
S = 4πr²
r = √( S / 4π )
r = √( 18.2π / 4π )
r = 2.13 cm
The diameter of the sphere is twice the radius, so:
d = 2r
d = 2( 2.13cm )
d = 4.26 cm
Therefore, the diameter of the sphere is 4.26 cm.
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Use the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1. Explain how you made your fractions without a number line so it says greater not lesser that is my question
The fraction 4/3 we get by using the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1
To make a fraction greater than 1 using the numbers 3 and 4, we can divide 3 by 4 and add 1.
3/4 + 1 = 7/4
The resulting fraction, 7/4, is greater than 1 because the numerator (7) is greater than the denominator (4).
We can also see this by writing 7/4 as a mixed number:
7/4 =[tex]1\frac{3}{4}[/tex]
The whole number part of the mixed number is 1, which means the fraction is greater than 1.
To make a fraction less than 1 using the same numbers, we can divide 4 by 3. This gives us:
4/3
The resulting fraction, 4/3, is less than 1 because the numerator (4) is smaller than the denominator (3).
We can also see this by writing 4/3 as a mixed number:
4/3 =[tex]1\frac{1}{3}[/tex]
The whole number part of the mixed number is 1, which means the fraction is less than 1.
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y=2x-6
x+y=3
graph it and get the solution