A doctor assigns people to treatment groups based on data from their medical records. Is this method of selecting treatment groups biased or unbiased?
Answers
9514 1404 393
Answer:
biased
Step-by-step explanation:
Any time a selection criterion is used that is other than a random draw, the selection is biased.
For a medical study, the bias may be intentional. The study may have the purpose of determining treatment efficacy based on age, gender, or previous medical history.
Related Questions
The equation k - 4a = -1 what would k be equal 2
Answers
Answer:
K=4a-1
Step-by-step explanation:
K = 4a- 1 (shifting -4a to right side from left)
At which values in the interval [0, 2TT) will the functions f(x) = cos 2x + 2 and g(x) = cos x + 1 intersect?
Answers
The functions f(x) and g(x) intersect at all values of x in the interval [0, 2π], except for x = π. So the answer is:
x ∈ [0, π) ∪ (π, 2π] (excluding x = π)<|endoftext|>
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
To find the values in the interval [0, 2π) where the functions f(x) = cos(2x) + 2 and g(x) = cos(x) + 1 intersect, we can set them equal to each other and solve for x:
cos(2x) + 2 = cos(x) + 1
First, let's subtract 1 from both sides to move all terms to one side of the equation:
cos(2x) + 1 = cos(x)
Now, let's rearrange the equation to get a single trigonometric function on one side:
cos(2x) - cos(x) + 1 = 0
Next, we can use the sum-to-product formula for cosine to simplify the equation:
2 sin(x/2) sin(3x/2) + 1 = 0
Now, we can subtract 1 from both sides:
2 sin(x/2) sin(3x/2) = -1
To proceed, we can divide both sides by 2:
sin(x/2) sin(3x/2) = -1/2
At this point, we can analyze the signs of sine functions. Since sine function has a range of [-1, 1], the only way for the product of two sines to be negative is if one of them is positive and the other is negative.
So we have two cases to consider:
Case 1: sin(x/2) > 0 and sin(3x/2) < 0
In this case, x/2 lies in the interval [0, π], and 3x/2 lies in the interval [0, 3π]. This means x must be in the interval [0, 2π].
Case 2: sin(x/2) < 0 and sin(3x/2) > 0
In this case, x/2 lies in the interval [π, 2π], and 3x/2 lies in the interval [0, π]. This means x must be in the interval [π, 2π].
So the values of x in the interval [0, 2π] where the functions f(x) and g(x) intersect are x ∈ [0, 2π] and x ∈ [π, 2π]. In other words, the functions intersect at all values of x in the interval [0, 2π], except for x = π.
Therefore, the functions f(x) and g(x) intersect at all values of x in the interval [0, 2π], except for x = π. So the answer is:
x ∈ [0, π) ∪ (π, 2π] (excluding x = π)<|endoftext|>
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find the exact value of the definite integral
Answers
Answer:
\(\displaystyle \int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta = \boxed{ \frac{7}{24} }\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Rule [Fundamental Theorem of Calculus 1]:
\(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)
Integration Methods: U-Substitution and U-Solve
Step-by-step explanation:
Step 1: Define
Identify given.
\(\displaystyle \int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta\)
Step 2: Integrate Pt. 1
Identify variables for u-substitution/u-solve.
Set u:\(\displaystyle u = \cos \theta\)[u] Differentiate [Trigonometric Differentiation]:
\(\displaystyle du = - \sin \theta \ d\theta\)[du] Rewrite [U-Solve]
\(\displaystyle d\theta = - \csc \theta \ du\)[Limits] Swap:
\(\displaystyle \left \{ {{ \theta = \frac{\pi}{3} } \atop { \theta = 0 }} \right. \rightarrow \left \{ {{ u = \cos \bigg( \frac{\pi}{3} \bigg) } \atop { u = \cos 0}} \right. \rightarrow \left \{ {{ u = \frac{1}{2} } \atop { u = 1 }} \right.\)
Step 3: Integrate Pt. 2
[Integrand] Rewrite:\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\\end{aligned}\)[Integral] Apply Integration Method [U-Solve]:
\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\& = \int\limits^{\frac{1}{2}}_0 {u^2 \sin \theta \csc \theta} \, du \\\end{aligned}\)[Integrand] Simplify:
\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\& = \int\limits^{\frac{1}{2}}_0 {u^2 \sin \theta \csc \theta} \, du \\& = \int\limits^{\frac{1}{2}}_0 {u^2} \, du \\\end{aligned}\)[Integral] Apply Integration Rule [Reverse Power Rule]:
\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\& = \int\limits^{\frac{1}{2}}_0 {u^2 \sin \theta \csc \theta} \, du \\& = \int\limits^{\frac{1}{2}}_0 {u^2} \, du \\& = \frac{u^3}{3} \bigg| \limits^{\frac{1}{2}}_0 \\\end{aligned}\)Apply Integration Rule [Fundamental Theorem of Calculus 1]:
\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\& = \int\limits^{\frac{1}{2}}_0 {u^2 \sin \theta \csc \theta} \, du \\& = \int\limits^{\frac{1}{2}}_0 {u^2} \, du \\& = \frac{u^3}{3} \bigg| \limits^{\frac{1}{2}}_0 \\& = \frac{\bigg( \frac{1}{2} \bigg) ^3}{3} - \frac{0}{3} \\\end{aligned}\)Evaluate:
\(\displaystyle \begin{aligned}\int\limits^{\frac{\pi}{3}}_0 {\cos^2 \theta \sin \theta} \, d\theta & = \int\limits^{\frac{\pi}{3}}_0 {\cos \theta \cos \theta \sin \theta} \, d\theta \\& = \int\limits^{\frac{1}{2}}_0 {u^2 \sin \theta \csc \theta} \, du \\& = \int\limits^{\frac{1}{2}}_0 {u^2} \, du \\& = \frac{u^3}{3} \bigg| \limits^{\frac{1}{2}}_0 \\& = \frac{\bigg( \frac{1}{2} \bigg) ^3}{3} - \frac{0}{3} \\& = \boxed{ \frac{7}{24} }\end{aligned}\)
∴ the exact value of the definite integral is equal to 7/24.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
3. A cube is made for 1 million cubic centimeters e What is the length of the side of the cube in centimeters? s = 1 cm
Answers
the answer is 1 million cm
The length of the side of the cube is 100 centimeters
What is volume ?
Volume is a three dimensional space occupy by the body of particular shape such as here :
The formula for volume of a cube is expressed as:
Volume, V = a³
Where, a is the length of its side
Given that the volume is 1 million cubic centimeters = 1, 000, 00
Substitute the values
1, 000, 000 = a³
Find the cube root of both sides
a = ∛10^6
a = 100 centimeters
Thus, the length of the side of the cube is 100 centimeters
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A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answers
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
Nick buys a pack of pokemon cards for $13.75. The tax is 5%. How much tax is added to the bill?
PLS HURY.
Answers
Answer:
The answer is
→ 69 cents in tax.
Step-by-step explanation:
$13.75 + 5% = $14.4375
$14.4375 - $13.75 = 0.6875 cents
0.6875 cents → 0.69 or 69 cents (rounded up)
Hope this helped! Mark him brainliest, he answered first! :^)
NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii
Answers
Answer:
7) Domain: (-∞, ∞)
Range: [-1, ∞)
8) Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 5From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
From inspection of the graph, the minimum y-value is y = -1.
The end behavior of the relation is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the range of the relation is restricted: [-1, ∞)
Question 6From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
The end behavior of the function is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
During a chemistry experiment, the volume of a solution increases when distilled water is added to the solution at a constant rate of 100 mL/min. Initially, there are 50 mL of solution, and water is added for 5 min.
Answers
Answer:
yes and there a r godd film?
Step-by-step explanation:
- 4/5w = -1 find w please
Answers
Answer:
The value of w = 4/5
Step-by-step explanation:
=> -4/5w = -1
=> -4 = -5w
=> 4 = 5w
=> w = 4/5
Answer:
5/4
Step-by-step explanation:
The fence around Wayne Manor is going to be replaced. No fence will be required on the side lying along Gotham River. If the new wrought iron fence costs $12 per meter for the side parallel to the river, and $4 per meter for the other two sides, find the dimensions of the maximum area that can be enclosed by the fence if Bruce Wayne cannot spend more than $3600.
Answers
Step-by-step explanation:
Let the side parallel to the river be x meter and the other two sides be of y meter, then
\(12 x+(2 y)(4)=3600\)
\(12 x+8 y &=3600\)
\(3 x+2 y &=900\)
\(2 y &=900-3 x\)
The area of the rectangle is \(A=xy \)
Substitute into to express the area in a single variable x as,
\(A(x) &=x\left[\frac{1}{2}(900-3 x)\right]\)
\(=\frac{1}{2}\left(900 x-3 x^{2}\right)\)
Differentiate A(x) with respect to x and equate to zero as,
\(A^{\prime}(x) &=0\)
\(\frac{d}{d x}\left[\frac{1}{2}\left(900 x-3 x^{2}\right)\right]=0\)
\(900-3(2 x) =0\)
x=150
Here, \(A^{\prime \prime}(x)=-3 x<0\) at \(x=150 \Rightarrow A\) is maximum
Therefore, the dimension is:
Length of side parallel to the river: x=150 m.
Length of other two side: \(y=\frac{1}{2}(900-450)=225\) m.
1- The acceleration of a particle is defined by the relation a = 6 ft/s 2. Knowing
that s =-32 ft when t = 0 and v= -6 ft/s when t = 2 s, determine the velocity, the
position, and the total distance traveled when t = 5 s.
help fast
Answers
Answer:
The initial velocity of the particle is
v' = -6 - 6.2 = -18 ft/s
at t = 5s, the velocity is v = -18 + 6.5 = 12 ft/s
the position is
\(x = - 32 - 18 \times 5 + \frac{1}{2} \times 6 \times 5 {}^{2} = - 47 \: ft\)
the total distance traveled is
\(s = | \frac{12 {}^{2} - 18 {}^{2} }{2 \times 6} | = 15 \: ft\)
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $40, plus $35 per hour. What is the slope of this situation?
80
65
40
35
Answers
Answer:
d. 35
Step-by-step explanation:
y = 35x + 40
The slope is 35 as 'm' is the slope of the equation
LMK IF IT WAS RIGHT!!
Answer:
D (35)
Step-by-step explanation:
The proportion of all US adults who eat popcorn when they go to the movie theater is p = 0.87. A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of p hat ?
a. The sampling distribution of p hat is approximately Normal because n p = 17.4 greater-than 10.
b. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. The sampling distribution of p hat is skewed right and centered at 0.87.
c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.
d. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the right.
Answers
The option that represents shapes of the sampling distribution of p hat is:
c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.
What is the shape of the sampling distribution?Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.
This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.
Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution is skewed to the left.
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
Progressive
Tax Rate
0-3000
2%
3001 - 5000
3%
5001 - 17,000
5%
17,001 and up
5.75%
Calculate the state income tax owed on a $90,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
Answers
Answer:
$4918
Step-by-step explanation:
You want the tax owed on $90,000 using the given tax rate table.
Tax computationThe tax is the sum of the amounts of tax due in each income range.
tax = 0.0575(90,000 -17,000) +0.05(17,000 -5000) +0.03(5000 -3000) +0.02(3000)
= 0.0575(90,000) -(17000(.0575 -.05) +5000(.05 -.03) +3000(.03 -.02))
= 0.0575(90,000) -(127.50 +100 +30)
= 5175 -257.50 = 4917.50
Rounded to the nearest dollar, the tax due is $4,918.
__
Additional comment
The tax will be the maximum of ...
0.02x0.03x -30 . . . . . . . . . . applicable over 30000.05x -130 . . . . . . . . . .applicable over 50000.0575x -257.50 . . . . applicable over 17000You can compute them all and find the maximum, or you can choose the function applicable to the income amount. The result is the same.
<95141404393>
There are 153 candies in a bag. Each candy has 4 calories. If you ate the whole bag, what is the best
estimate for how many calories you consumed?
Answers
Answer:
612 calories
Step-by-step explanation:
153 x 4 = 612
Answer:
612 calories
Step-by-step explanation:
what I would do is multiply 153×4=612 calories
Genesis throws a ball up in the air. The graph below shows the height of the ball hh in meters after tt seconds. Find the interval for which the ball’s height is decreasing.
help please
Answers
We conclude that the interval in which the function decreases is (1.5, 3]
In which interval is the ball's height decreasing?
The ball is decreasing when the graph, reading from left to right, is going downwards.
Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.
And we can see that the vertex is at x = 1.5
And we also see that the graph of the function ends at x = 3.
Then we conclude that the interval in which the function decreases is (1.5, 3]
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Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3 of the remaining cookies, and when Carla came home, she ate 1/2 of the cookies on the plate. When their mother came home, there were 5 cookies on the plate. How many did each child eat?
Answers
Answer: Children ate 15 cookies and 5 each because Alex ate 1/4 and bernice ate 1/3 and carla ate 1/2
and 5 were left
5 into 3 is 20
and 5 are left so
20-5 is 15
15 divide by 3 is 5
Frame calculation process in your words but the final answer is each child ate 5 cookies.
PLEASE HELP ME PLEASE PLEASE PLEASE
Initially as x incrases y (increases or decreases)
The slope of the graph is equal to ____ for all x between x= 0 and x=3
Starting at x=3 the function value y (increases or decreases) as x increases
The slope of the graph is equal to _____ for x between x=3 and x=5
For x between x=0 and x=4, the function value of y is (≤ or ≥ or =)
For x between x=4 and x=8 the function of value y is (≤ or ≥ or =)
Answers
The slope of the graph is equal to 1 for all x between x= 0 and x=3.
Starting at x=3 the function value y increases as x increases.
The slope of the graph is equal to 3 for x between x=3 and x=5
For x between x=0 and x=4, the function value of y is ≤ 0.
For x between x=4 and x=8 the function of value y is ≥ 0.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (0 - 3)/(3 - 0)
Slope (m) = -3/3
Slope (m) = -1.
For x between x=3 and x=5, the slope is given by;
Slope (m) = (3 + 3)/(5 - 3)
Slope (m) = 6/2
Slope (m) = 3.
By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.
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Joseph is 33 years old. Five years ago, He was twice as old as Ann. How old will Ann be in 5 years time?
Answers
Answer:
19 years oldStep-by-step explanation:
\(Joseph = 33 \:years \:old\\ \\Let \: ann's \:age be x\\\\33-5 = 2x\\\\28 = 2x\\\\Divide \:both \:sides \:of \:the \:equation \: by \:2\\\\\frac{2x}{2} = \frac{28}{2} \\\\x = 14\\\\Ann's \:present \:age \:= 14\\\\In \:5 \:years \:time ; \\\\14+5 = 19\\\)
Owen has twice as many marbles as his friend Ric. If Owen has 21 marbles, how many marbles does Ric have?
Answers
Answer:
Ric has 42 marbles.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Owen = x marbles
Ric = 2x marbles
x = 21 marbles
Step 2: Find
Substitute in x: 2(21 marbles)Multiply: 42 marblesI dont understand how to do this precalc question
Answers
Answer:
x-intercept: (-0.1, 0)Horizontal Asymptote: y = -3Exponential growth(First answer option)
Step-by-step explanation:
General form of an exponential function
\(y=ab^x+c\)
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form:If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function. y=c is the horizontal asymptote.x is the independent variable.y is the dependent variable.
Given exponential function:
\(y=4(10)^x-3\)
x-interceptThe x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:
\(\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}\)
Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.
AsymptoteAn asymptote is a line that the curve gets infinitely close to, but never touches.
The parent function of an exponential function is:
\(f(x)=b^x\)
As x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.
Therefore, there is a horizontal asymptote at y = 0.
This means that a function in the form \(f(x) = ab^x+c\) always has a horizontal asymptote at y = c.
Therefore, the horizontal asymptote of the given function is y = -3.
Exponential Growth and DecayA graph representing exponential growth will have a curve that shows an increase in y as x increases.
A graph representing exponential decay will have a curve that shows a decrease in y as x increases.
The part of an exponential function that shows the growth/decay factor is the base (b).
If b > 1 then it is an increasing function.If 0 < b < 1 then it is a decreasing function.The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.
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The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answers
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
The distance travelled by a car during 10 minutes moving with a speed of 10 meter per second is
Answers
Answer:6000 meters
Step-by-step explanation:
10 x 60=600
600 x 10=6000
10m/s =d/10
d=10x10
d= 100 m
The car travels 100m in 10 minutes
Checking it :
10=100/10
100/10=10
Thus proved
Estimate the slope of the tangent line (rate of change) to f(x) = ² at x = -1 by finding the slopes of
the secant lines through the points:
a. (-2,4) and (0,0)
secant slope, msec=
b. (-1.5, 2.25) and (-0.5, 0.25)
secant slope, msec=
Answers
a. The secant slope through (-2,4) and (0,0) is -2.
b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.
The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.
To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.
a. (-2,4) and (0,0):
The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:
msec = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
msec = (0 - 4) / (0 - (-2))
= -4 / 2
= -2
So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.
b. (-1.5, 2.25) and (-0.5, 0.25):
The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:
msec = (0.25 - 2.25) / (-0.5 - (-1.5))
= (-2) / (1)
= -2
So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.
By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.
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You deposit $300 in an account that earns simple interest at an annual rate of 6.5%.
If no other deposits or withdrawals were made, what is the total amount of money in the account at the end of 8 years?
Answers
Total amount of money in the account will be $456.
How much money will be in the account after 8 years?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.
The formula for simple interest is: Simple Interest = Principal × Rate × Time
Principal (P) is $300
Rate (R) is 6.5%
Time (T) is 8 years.
Simple Interest = $300 × 0.065 × 8
Simple Interest = $156
Total Amount = Principal + Simple Interest
Total Amount = $300 + $156
Total Amount = $456.
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consider the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1). the fourth vertex lies above the point (0,0) at height 1. see the picture below a tetrahedron as described in the problem setup an integral the represents the volume of the tetrahedron then evaluate it.
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The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The integral that represents the volume of the tetrahedron is given by:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$$
Evaluating the integral, we get:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx = \int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx = \int_0^1 \frac{1}{2} (1-x)^2\,dx = \frac{1}{6}$$
Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
We first set up the integral that represents the volume of the tetrahedron. The integral is a triple integral, so it can be written as $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$. This integral is the volume of a 3-dimensional region enclosed by the limits $x \in [0,1]$, $y \in [0,1-x]$, and $z \in [0,1-x-y]$. This region is exactly the same as the volume of the tetrahedron because it is the same 3-dimensional region.
Next, we evaluate the integral. First, we integrate with respect to $z$, which gives us $\int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx$. Then, we integrate with respect to $y$, which gives us $\int_0^1 \frac{1}{2} (1-x)^2\,dx$. Finally, we integrate with respect to $x$, which gives us $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
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The middle school choir concert was 5/6 of an hour long. Each song was 1/12 of an hour. How many songs did the audience hear during the choir concert?
Answers
Answer:
The answer is 10 Songs
Step-by-step explanation:
Total hour=5/6=5/6×60=50min
Each song=1/12=1/2×60=5mins
Number of song sang=Total hour/Each song sang
N=50/5=10 songs
Which best describes the value of 8 in 3.458?
Since 8 is in the thousandths place, the value of the digit is 0.008.
Since 8 is in the hundredths place, the value of the digit is 0.08.
O Since 8 is in the thousandths place, the value of the digit is 0.08.
Since 8 is in the hundredths place, the value of the digit is 0.008.
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Answer:
Since 8 is in the thousandths place, the value of the digit is 0.008.
um I hope that's correct.
let days-on-the-market be the dependent variable and price be the independent variable. b-1. determine the regression equation
Answers
To determine the regression equation, we need to fit a line to the data that best describes the relationship between the dependent variable and the independent variable. The equation of the line is typically expressed in the form:
y = a + bxwhere y is the dependent variable, x is the independent variable, a is the y-intercept (the point at which the line crosses the y-axis), and b is the slope of the line (the rate of change of y with respect to x).
If we determine that a = 10 and b = 0.5, the regression equation would be:
Days-on-the-market = 10 + 0.5 * priceThis equation describes the relationship between the dependent variable (days-on-the-market) and the independent variable (price). It tells us that for every unit increase in price, the number of days on the market is expected to increase by 0.5.
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Prove that (- 1 + i)^7 = -8(1 + i)
Answers
Convert \(-1+i\) to polar form.
\(z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}\)
By de Moivre's theorem,
\(\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)\)
QED