Answer:
c) Multistage sampling.In statistics, there are several strategies to select a sample. Remember that a sample is a sub group selected from a population. This sample selection must be random to have more reliability in the research, each answer option represents a type of sampling.
In this case, the researcher is using a multistage sampling, because it consists in taking smaller sample units at each stage, which is being done in this example. First, is selected a number of counties, then the precincts, and at the end the voters. By this way, the sample is being reduced to less subjects at each stage.
The sampling strategy described is an example of c) multistage sampling. This technique helps in reducing complexity and cost.
The sampling strategy described in the question is an example of multistage sampling.
In this process:
A simple random sample of 10 counties in Pennsylvania is selected.From each of these counties, 10 precincts are chosen randomly.Finally, from each of these 100 precincts, a simple random sample of 20 voters is selected.This results in a final sample of 2,000 voters.Multistage sampling is used to reduce the complexity and cost of data collection by breaking the population into smaller groups at each stage.
The annual interest on an $20,000 investment exceeds the interest earned on a $4000 investment by $1320. The $20,000 is invested at a 0.6% higher rate of interest than the $4000. What is the interest rate of each investment?$20,000 is invested at what %$4,000 is invested at what %
The interest rate for the $4000 investment is approximately 2.1% and for the $20000 investment, it is approximately 2.7%.
Explanation:This problem can be solved using the concept of simple interest. Let's denote the interest rate of the $4000 investment as r (in decimal form) and the interest rate of the $20000 investment would be r+0.006. Now, we can set up our equations based on the information given:
1. For $4000 investment: Interest = 4000 * r
2. For $20000 investment: Interest = 20000 * (r + 0.006)
It is also given that the interest earned from the $20000 investment is $1320 more than the $4000 investment. Therefore, we can set up a third equation as:
20000 * (r + 0.006) - 4000 * r = 1320
By solving this equation, we find that r (corresponding to the $4000 investment) is approximately 0.021 or 2.1% and therefore, the interest rate for the $20000 investment is roughly 2.7% (2.1% + 0.6%).
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A wire is to be cut into two pieces. One piece will be bent into a square, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 64 cm2,
what is the minimum length of wire that can be used?
What is the maximum length of wire that can be used?
Answer:
minimum: 28.36 cmmaximum: 42.76 cmStep-by-step explanation:
The relationships between the radius of a circle and its circumference and area are ...
C = 2πr
A = πr²
The relationships between the side length of a square and its perimeter and area are ...
P = 4s
A = s²
So, the length of wire will be ...
w = C + P
w = 2πr + 4s
subject to the constraint that the sum of areas is 64 cm²:
πr² + s² = 64
___
Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.
L = 2πr + 4s + λ(πr² +s² -64)
∂L/∂r = 0 = 2π +2πλr . . . . . . [eq1]
∂L/∂s = 0 = 4 +2λs . . . . . . . . [eq2]
∂L/∂λ = 0 = πr² +s² -64 . . . . [eq3]
__
Solving for λ, we find ...
0 = 1 +λr . . . . divide [eq1 by 2π
λ = -1/r . . . . . . subtract 1, divide by r
Substituting into [eq2], we get ...
0 = 4 + 2(-1/r)s
s/r = 2 . . . . . . . . . .add 2s/r and divide by 2
This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.
Substituting the relation s=2r into the area constraint, we find ...
πr² +(2r)² = 64
r = √(64/(π+4)) = 8/√(π+4) ≈ 2.99359 . . . . cm
and the maximum wire length is ...
2πr +4(2r) = 2r(4+π) = 16√(4+π) ≈ 42.758 . . . cm
_____
The minimum wire length will be required when the entire area is enclosed by the circle. In that case, ...
πr² = 64
r = √(64/π)
C = 2πr = 2π√(64/π) = 16√π ≈ 28.359 . . . cm
_____
Comment on the solution method
The method of Lagrange multipliers is not needed to solve this problem. The alternative is to write the length expression in terms of one of the figure dimensions, then differentiate with respect to that:
w = 2πr + 4√(64-πr²)
dw/dr = 2π -4πr/√(64-πr²) = 0
64 -πr² = 4r²
r = √(64/(π+4)) . . . . same as above
_____
Comment on the graph
The attached graph shows the relationship between perimeter and circumference for a constant area. The green curve shows the sum of perimeter and circumference, the wire length. The points marked are the ones at the minimum and maximum wire length.
The minimum length of the wire can be found by setting up a function to represent the total length of the wire and using calculus to minimize it. The maximum length of the wire is undefined because the length of the wire can increase indefinitely as the radius of the circle decreases.
Explanation:To solve this problem, we use the formulas for the perimeters of a square and a circle, and the fact that the sum of their areas should equal 64 cm2. The perimeter of a square is 4s and the circumference of a circle is [tex]2\pi r[/tex], where s and r represent the side length of the square and the radius of the circle, respectively. The area of a square is s2 and the area of a circle is πr2.
The total length of the wire is the sum of the perimeter of the square and the circumference of the circle. The total area enclosed by the wire, according to the problem, should be 64 cm2.
To find the minimum length of wire needed, we can use calculus to minimize the function representing the length of the wire. The maximum length of the wire is undefined because as the radius of the circle approaches zero, the side length of the square and therefore the length of the wire can increase indefinitely.
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If Ben borrowed $20,000 for his business of a 10-year loan at 6.25%.
a. What is the monthly payment of a Ben’s loan?
b. What will be the total of Ben’s monthly payments for the 10 years?
c. How much total interest did Ben pay for the loan?
Answer:
a. $104.17 monthly interest.
b. 120 monthly payments.
c. Total interest of $12,500.
Step-by-step explanation:
a.
I = Prt
I = (20000 x 0.0625 x 1) = 1250 annually
for monthly Interest payment divide the answer by 12;
1250/12 = $104.17 monthly
b.
12 x 10 = 120 monthly payments
c.
I = Prt
I = $20,000 x 0.0625 x 10
I = $12,500
On a drive from one city to another, Victor averaged 5151 mph. If he had been able to average 7575 mph, he would have reached his destination 88 hrs earlier. What is the driving distance between one city and the other?
Answer:
d=1.416.525 mile
Step-by-step explanation:
V1=5151m/h, t1=t, V2=7575m/h, t2=t-88h
d1=d2 Because it is same distance; V1=d1/t and V2=d2/(t-88) but d1=d2
d=V1t=V2(t-88) → 5151t=7575(t-88) → 5151t=7575t-666.600 → 7575t-5151t=666.600 → 2424t=666.600 → t=666.600/2424 → t=275h so
[tex]d=5151\frac{mile}{h}.275h = 1.416.525mile[/tex]
If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e−t/50. What is the average temperature (in degrees Celsius) of the coffee during the first half hour?
Answer:
61°C
Step-by-step explanation:
Newton's Law of cooling gives the temperature -time relationship has:
T (t) = 20 + 75 е⁻(t/50)-------------------------------------------------------- (1)
where Time is in minutes (min) & Temperature in degree Celsius (°C)
During the first half hour, t = 30 mins
Substituting into (1)
T = 20 + 75 е⁻(30/50)
= 20 + 75(0.5488)
= 20 + 41.16
= 61.16°C
≈ 61°C
Plz explain and prove the triangles congruence.
Answer:
(3) ∠BCA ≅ ∠DAC
Step-by-step explanation:
BC and AD are parallel. AC is a transversal line passing through both lines. That means ∠BCA and ∠DAC are alternate interior angles. Therefore, they are congruent.
can anyone help me? I've been stuck with this problem for hours
Answer:
336.02 square centimeters
Step-by-step explanation:
The surface area is the area of all the surfaces of the prism shown.
The prism has 7 surfaces.
Top and Bottom are pentagons with side lengths of 5.
The other 5 side surfaces are rectangles with length 10 and width 5.
Note the formulas of area of pentagon and area of rectangle below:
Area of Rectangle = Length * Width
Area of Pentagon = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2[/tex] , where a is the side length
Lets find area of each of the surfaces:
Top Surface (Pentagon with side length 5) = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01[/tex]
Bottom Surface = same as Top Surface = 43.01
Side Surface (rectangle with length 10 and width 5) = 10 * 5 = 50
There are 5 side surfaces that are each 50 sq. cm. so area would be:
Area of 5 Side Surface = 5 * 50 = 250
Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters
Give the coordinates for the image of R (0, -5) E (4, -3) C (6, -5) T (2, -7) when it is reflected across the line y = x.
Answer:
Below.
Step-by-step explanation:
The x and y coordinates flip with this reflection e, g (2, 1) goes to (1, 2).
So R (0, -5) ---> R' (-5, 0).
E (4, -3) ---> E' (-3, 4).
C (6, -5) ---> C' (-5, 6).
T (2, -7) ---> T' (-7, 2).
Marco is making Mosaic garden tools using red yellow and blue tiles. He has 45 red tiles, 90 blue tiles, and 75 yellow tiles. Each Stone must have the same number of each color tile. How many of each color tile will Marco use in each stone if the greatest number of stones he can make is 45?
Answer:
Marco will use [tex]1[/tex] red tile, [tex]2[/tex] blue tiles and [tex]1\frac{2}{3}[/tex] yellow tiles in each stone.
Step-by-step explanation:
Given:
Number of red tiles = 45
Number of blue tiles = 90
Number of yellow tiles = 75
Greatest number of stones that Marco can make = 45
To determine how many each color tile Marco will use in each stone.
Solution:
In order to determine the number of each color tile in each stone we need to divide total number of a particular tile by total number of stones. By doing this we can get the exact number of that color tile used in each stone.
Number of red tile in each stone
⇒ [tex]\frac{\textrm{Total number of red tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{45}{45}=1[/tex]
Number of blue tiles in each stone
⇒ [tex]\frac{\textrm{Total number of blue tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{90}{45}=2[/tex]
Number of yellow tile in each stone
⇒ [tex]\frac{\textrm{Total number of yellow tiles}}{\textrm{Total number of stones}}[/tex]
⇒ [tex]\frac{75}{45}[/tex]
⇒ [tex]\frac{5}{3}[/tex] [Reducing to simpler fraction by dividing both numbers by their GCF=15]
⇒ [tex]1\frac{2}{3}[/tex] [Converting improper fraction to mixed number]
∴ Marco will use [tex]1[/tex] red tile, [tex]2[/tex] blue tiles and [tex]1\frac{2}{3}[/tex] yellow tiles in each stone.
Answer:
Marco will use 3 red, 6 blue and 5 yellow tiles on each stones
Explanation:
Given, each stone must have same number of each colour tile
Then, calculating the highest common factors of the number HCF (45, 90, 75)
Factors of 45 = 3 × 3 × 5
Factors of 90 = 2 × 3 × 3 × 5
Factors of 75 = 3 × 5 × 5
Highest Common Factors (HCF) = 3 × 5 = 15
Dividing all three numbers by 15, we get
Red Tiles =[tex]\frac{45}{15}[/tex] = 3
Blue Tiles = [tex]\frac{90}{15}[/tex] = 6
Yellow Tiles = [tex]\frac{75}{15}[/tex] = 5
Therefore, Marco will use 3 red, 6 blue and 5 yellow tiles on each stones
The first term of an arithmetic sequence is equal to four and the common difference is three. find the formula for the value of the nth term
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
Step-by-step explanation:
The formula of the nth term in the arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first term of the sequenced is the common difference between each two consecutive terms∵ The first term of an arithmetic sequence is equal to four
∴ a = 4
∵ The common difference is equal to three
∴ d = 3
- Substitute these values in the rule of the nth term
∵ [tex]a_{n}=a+(n-1)d[/tex]
∴ [tex]a_{n}=4+(n-1)3[/tex]
- Simplify it
∴ [tex]a_{n}=4+3n-3[/tex]
∴ [tex]a_{n}=1+3n[/tex]
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
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A manufacturer knows that their items have a normally distributed length, with a mean of 10.9 inches, and standard deviation of 1.2 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?
Answer:
The probability that their mean length is less than 11.2 inches is 0.5987
Step-by-step explanation:
Mean = 10.9 inches
Standard deviation = 1.2 inches
We are supposed to find If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
We are supposed to find P(x<11.2)
[tex]Z=\frac{11.2-10.9}{1.2}[/tex]
[tex]Z=0.25[/tex]
Refer the z table for p value
p value = 0.5987
Hence the probability that their mean length is less than 11.2 inches is 0.5987
A manufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 2%. A random sample of 250 lenses contains 6 defective lenses.
(a) Formulate and test an appropriate set of hypotheses to determine whether the machine can be qualified. Use α = 0.05. Find the P-value.
(b) Explain how the question in part (a) could be answered with a confidence interval. 9-97. A researcher claims th
Answer:
Does not exceed 2% in both cases.
Step-by-step explanation:
Given that a manufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 2%.
Sample proportion = [tex]\frac{6}{250} \\=0.024[/tex]
Create hypothesses as
[tex]H_0: p = 0.02\\H_a : p >0.02[/tex]
(Right tailed test at 5% significance level)
P difference = 0.004
Std error = 0.0089
test statistic Z = p diff/std error = 0.4518
p value = 0.326
Since p >alpha, we accept nullhypothesis
b) For confidence interval 97% we have
Margin of error = 2.17* std error = 0.0192
Confidence interval
= [tex](0.024-0.0191, 0.024+0.0191)\\= (0.0049, 0.0431)\\[/tex]
Since 2% = 0.02 lies within this interval we accept null hypothesis.
Does not exceed 2%
Since
Final answer:
To determine whether the new grinding machine can be qualified, we need to test the hypothesis that the percentage of polished lenses with surface defects does not exceed 2%.
Explanation:
To determine whether the new grinding machine can be qualified, we need to test the hypothesis that the percentage of polished lenses with surface defects does not exceed 2%. The null hypothesis (H₀) is that the proportion of defective lenses is equal to or less than 2%, while the alternative hypothesis (Ha) is that the proportion of defective lenses is greater than 2%. We can use a one-sample proportion test to analyze the data.
(a) The hypotheses are:
H₀: p ≤ 0.02 (proportion of defective lenses)
Ha: p > 0.02 (proportion of defective lenses)
With a significance level of α = 0.05, we can calculate the p-value from the sample data. Using a normal approximation to the binomial distribution, we find that the p-value is 0.0165.
(b) The question in part (a) can also be answered using a confidence interval. We can calculate a confidence interval for the proportion of defective lenses and see if it includes or excludes the value of 0.02. If the confidence interval includes 0.02, it suggests that the machine can be qualified. If the confidence interval does not include 0.02, it suggests that the machine cannot be qualified.
2 questions geometry :) thanks if you answer
Answer:
Part 1) An expression for the x-coordinate of T is (a+2)
Part 2) The value of x=39 ft (see the explanation)
Step-by-step explanation:
Part 1)
step 1
we know that
The rule of the reflection of a point across the x-axis is equal to
[tex](x,y) -----> (x,-y)[/tex]
Apply the rule of the reflection across the x-axis to the Q coordinates
Q (a,b) ----------> Q'(a,-b)
step 2
The translation is 2 units to the right
so
The rule of the translation is
(x,y) ----> (x+2,y)
Apply the rule of the translation to the Q' coordinates
Q'(a,-b) -----> T(a+2,-b)
therefore
An expression for the x-coordinate of T is (a+2)
Part 2)
we know that
A reflection is a rigid transformation, the image is the same size and shape as the pre-image
In this problem the floor plan house A and the floor house B have the same size and shape
That means that its corresponding sides and corresponding angles are congruent
therefore
The value of x=39 ft
For each cost function (given in dollars), find (a) the cost,average cost, and marginal cost at a production level of 1000units; (b) the production level that will minimize the averagecost; and c) the minimum average cost.C(x)= 16,000x + 200x+ 4x3/2
Answer:
a) $342,491
$342.491
$389.74
b) $400
c) $320
Step-by-step explanation:
the cost function = C(x)
C(x) = 16000 + 200x + 4x^3/2
a) when we have a unit of 1000 unit, x= 1000
C(1000) = 16000 + 200(1000) + 4(1000)^3/2
= 16000 + 200000 + 126491
= 342,491
Cost = $342,491
Average cost= C(1000) / 1000
= 342,491/1000
= 342.491
The average cost = $342.491
Marginal cost = derivative of the cost
C'(x) = 200 + 4(3/2) x^1/2
= 200 + 6x^1/2
C'(1000) = 200 + 6(1000)^1/2
= 389.74
Marginal cost = $389.74
Marginal cost = Marginal revenue
C'(x) = C(x) / x
200 + 6x^1/2 = (16000 + 200x + 4x^3/2) / x
200 + 6x^1*2 = 16000/x + 200 +4x^1/2
Collect like terms
6x^1*2 - 4x^1/2 = 16000/x + 200 -200
2x^1/2 = 16000/x
2x^3/2 = 16000
x^3/2 = 16000/2
x^3/2 = 8000
x = 8000^2/3
x = 400
Therefore, the production level that will minimize the average cost is the critical value = $400
C'(x) = C(x) / x
C'(400) = 16000/400 + 200 + 4(400)^1/2
= 40 + 200 + 80
= 320
The minimum average cost = $320
1.what is the length of the segment joining 3,6 and -2,-6
2.what is the center of the circle (x+6)^2+(y-8)^2=144
3.what is the slope of the line 3y+2x-6=0
1.what is the length of the segment joining 3,6 and -2,-6 : 13 units
2.what is the center of the circle (x+6)^2+(y-8)^2=144 => (-6,8)
3.what is the slope of the line 3y+2x-6=0=> -2/3
Step-by-step explanation:
1.what is the length of the segment joining (3,6) and (-2,-6)?
Let
(x1,y1) = (3,6)
(x2,y2) = (-2,-6)
The length of a segment is given by:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Putting\ values\\d = \sqrt{(-2-3)^2+(-6-6)^2}\\d = \sqrt{(-5)^2+(-12)^2}\\= \sqrt{25+144}\\= \sqrt{169}\\=13\ units[/tex]
2.what is the center of the circle (x+6)^2+(y-8)^2=144
The equation of circle is given by:
[tex](x-h)^2+(y-k)^2 = r^2[/tex]
Here, h and k are the coordinates of centre of circle
x - h = x+6
-h = 6
h = -6
y - 8 = y - k
-8 = - k
k = 8
So,
The center of circle is: (-6,8)
3.what is the slope of the line 3y+2x-6=0
We have to convert the equation in slope-intercept form to find the slope
Slope-intercept form is:
y = mx+b
Now,
[tex]3y+2x-6=0\\3y+2x = 6\\3y = -2x+6[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3} = -\frac{2}{3}x+\frac{6}{3}\\y = -\frac{2}{3}x + 2[/tex]
In slope-intercept form, the co-efficient of x is the slope of the line so
m = -2/3
Keywords: Coordinate geometry, Slope
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Find the y-intercept of each line defined below and compare their values.
Answer:
Y - intercept of equation of-line A is y = 1.
Y - intercept of equation of-line B is y = -2.
Step-by-step explanation:
Given:
For Iine A:
[tex]y+ 1 =\frac{1}{5}\times (x+10)[/tex]
For line B:
x = -2 then y = 2
x = -1 then y = 0
x = 0 then y = -2
x = 1 then y = -4
To Find:
Y- intercepts of Line A and Line B.
Solution:
Intercepts: Where the line cut X axis called X- intercept and where cut Y axis is called Y- intercept.
Y-intercept mean x coordinate will be 0
Therefore Put x = 0 in Line A we get
[tex]y+ 1 =\frac{1}{5}\times (0+10)\\y+1=\frac{10}{5}\\ y+1=2\\y= 2-1\\y=1[/tex]
Y - intercept of equation of-line A is y = 1.
For line B
See where x coordinate is 0 ,Therefore we have,
y = -2
Y - intercept of equation of-line B is y = -2.
Clara has driven 70,000 miles in her car. On average, she drives 26 miles every day. Write a rule that represents her miles driven m as a function of time d.
Answer:
[tex]m(d)=26\ d[/tex]
where [tex]m[/tex] represents miles driven
and [tex]d[/tex] represents number of days driven.
Step-by-step explanation:
Given:
Total distance driven in miles = 70,000
Average distance driven each day = 26 miles
Taking average as unit rate of miles covered per day.
∴ we can say the car covers 26 miles per day.
Using unitary method to find miles driven in [tex]d[/tex] days.
In 1 day miles driven = 26
In [tex]d[/tex] days miles driven = [tex]26\times d =26\ d[/tex]
So, to find [tex]m[/tex] miles driven the expression can be written as:
[tex]m(d)=26\ d[/tex]
rewrite the following radical expressions as equivalent exponential expressions with a positive exponent square root 5
Answer:
You didn't write the expression
Step-by-step explanation:
A particle whose mass is 4 kg moves in xyplane with a constant speed of 2 m/s in the positive x-direction along y = 6 m. Find the magnitude of its angular momentum relative to the point (x0, y0), where x0 = 0.9 m and y0 = 10 m. Answer in units of kg m2 /s.
The magnitude of the angular momentum of the particle relative to the point (0.9 m, 10 m) is [tex]{\text} 32.8 kg m^2/s[/tex].
Angular momentum is a physical quantity that measures the rotational motion of an object or system.
Given:
Mass = 4 kg,
velocity = 2 m/s
The following equation provides the particle's angular momentum (L):
L = mvr
where:
m = mass
v = velocity of the particle
r = perpendicular distance
To find the magnitude of the angular momentum relative to the point point [tex](x_0, y_0)[/tex], where [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m.
To find the perpendicular distance (r), use the distance formula:
[tex]r = \sqrt{((x - x0)^2 + (y - y0)^2)[/tex]
Substituting the values [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m in above formula
[tex]r = \sqrt{((0 - 0.9)^2 + (6-10)^2)[/tex]
= [tex]\sqrt{((-0.9)^2 + (-4)^2)[/tex]
= √(0.81 + 16)
= √16.81
= 4.1 m
Now, the angular momentum (L) using the formula:
L = mvr
L = 4 kg x 2 m/s x 4.1 m
L = 32.8 kg
As a result, the particle's angular momentum is [tex]{\text} 32.8 kg m^2/s[/tex].
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The magnitude of the angular momentum relative to a point (x0, y0) depends on the moment of inertia and angular velocity of the particle. However, in this case, the angular velocity is undefined, so the magnitude of the angular momentum is also undefined.
Explanation:The angular momentum of a particle can be calculated by multiplying its moment of inertia with its angular velocity. In this case, the particle has a mass of 4 kg and moves with a constant speed of 2 m/s in the positive x-direction. To find the magnitude of its angular momentum relative to the point (x0, y0), we need to calculate the moment of inertia and angular velocity. Since the particle is moving in the xy-plane, we can calculate the distance of the particle from the point (x0, y0) and use it to find the angular momentum. The magnitude of the angular momentum can be calculated by dividing the cross product of the position vector and linear momentum with the mass of the particle.
First, let's calculate the moment of inertia (I) of the particle. The moment of inertia can be calculated using the formula I = mr², where m is the mass of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle is moving in the xy-plane, so the distance of the particle from the point (x0, y0) can be calculated using the distance formula: d = sqrt((x-x0)² + (y-y0)²). Substituting the values, we have d = sqrt((0-0.9)² + (6-10)²) = sqrt(13.21) = 3.63 m. The moment of inertia can be calculated as I = 4 kg * (3.63 m)² = 52.60 kg*m².
Next, let's calculate the angular velocity (ω) of the particle. The angular velocity can be calculated using the formula ω = v/r, where v is the linear velocity of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle has a constant speed of 2 m/s in the positive x-direction along y = 6 m, so the distance of the particle from the axis of rotation is the distance from the point (0, 6). Substituting the values, we have r = sqrt((0-0)² + (6-6)²) = sqrt(0) = 0 m. The angular velocity can be calculated as ω = 2 m/s / 0 m = undefined. Since the angular velocity is undefined, the magnitude of the angular momentum relative to the point (x0, y0) is also undefined.
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determine whether the graph is the graph of a function
yes or no?
Answer:
yes
Step-by-step explanation:
The graph passes the vertical line test, so is the graph of a function (yes). Each input value has exactly one output value.
A 150 km trip was covered by a motorcycle going at an average speed of 75 km/h, by a bus doing 60 km/h, by a truck doing 50 km/h, and by a bicycle doing 20 km/h. What is the constant of variation?
Answer:
Step-by-step explanation:
Motrcycle: 2 hours 150/75 = 2 hours
Bus: 150/60= 2.5 hours
Truck:150/50= 3 hours
Bike:= 150/20= 7.5 hours
I= nE/nr+R , solve for n
For this case we have the following equation:
[tex]I = \frac {nE} {nr + R}[/tex]
We must clear the variable "n", for them we follow the steps below:
We multiply by [tex]nr + R[/tex] on both sides of the equation:
[tex]I (nr + R) = nE[/tex]
We apply distributive property on the left side of the equation:
[tex]Inr + IR = nE[/tex]
Subtracting [tex]nE[/tex] from both sides of the equation:
[tex]Inr-nE + IR = 0[/tex]
Subtracting IR from both sides of the equation:
[tex]Inr-nE = -IR[/tex]
We take common factor n from the left side of the equation:
[tex]n (Ir-E) = - IR[/tex]
We divide between Ir-E on both sides of the equation:
[tex]n = - \frac {IR} {Ir-E}[/tex]
Answer:
[tex]n = - \frac {IR} {Ir-E}[/tex]
I plan on opening a savings account with $800 and leaving it in the account for 4 years. If the bank is going to pay me an interest rate of 5%, how much money will I have in the account at the end of 4 years? A. $2,400 B. $1,600 C. $960 D. $160
Answer:
i would think that its c
let me know if its wrong
Answer:
c
Step-by-step explanation:
i know
Usually, Dolores has to stock the shelves by herself and it takes her 7.2 hours. Today Camille helped Dolores and they were able to finish the task in 2.8 hours. How long would it have taken Camille if she were working alone?
Step-by-step explanation:
Let w be the work of stock the shelves and t be the time for Camille to the worl alone.
Dolores takes 7.2 hours.
[tex]\texttt{Rate of Dolores = }\frac{w}{7.2}[/tex]
[tex]\texttt{Rate of Camille = }\frac{w}{t}[/tex]
If they combine work is completed in 2.8 hours.
That is
[tex]2.8=\frac{w}{\frac{w}{7.2}+\frac{w}{t}}\\\\2.8=\frac{7.2t}{t+7.2}\\\\2.8t+20.16=7.2t\\\\4.4t=20.16\\\\t=4.58hours[/tex]
It takes 4.58 hours to stock the shelves if Camille were working alone
No yes no @ 90, 9, 0,-90,-9 @ 25, 11, -8, -7, -15 @ 4, 2, 0, -2, -4, -42 MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E Em56 O Creative Publications 4-R - 34-M
Answer:
Step-by-step explanation:
what?
pls help me finna mark brainliest
The right answer is Option D.
Step-by-step explanation:
Given,
Total people surveyed = 250
Total people who prefer sports channel= 62
Percent of people who prefer sports channel;
Percent = [tex]\frac{people\ who\ prefer\ sports\ channel}{Total\ no.\ of\ people\ surveyed}*100[/tex]
[tex]Percent=\frac{62}{250}*100\\\\Percent=\frac{6200}{250}\\\\Percent= 24.8\%[/tex]
24.8% of everyone surveyed preferred sports channel.
The right answer is Option D.
Keywords: percentage, division
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A textbook search committee is considering 19 books for possible adoption. The committee has decided to select 7 of the 19 for further consideration. In how many ways can it do so?
It can be done in 50388 ways
Step-by-step explanation:
When the selection has to be made without order, combinations are used.
The formula for combination is:
[tex]C(n,r) =\frac{n!}{r!(n-r)!}[/tex]
Here
Total books = n =19
Books to be chosen = r = 7
Putting the values
[tex]C(19,7) = \frac{19!}{7!(19-7)!}\\\\=\frac{19!}{7!12!}\\\\=50388\ ways[/tex]
It can be done in 50388 ways
Keywords: Combination, selection
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Olga Decorat blankets with ribbon she has 12 yards of ribbon she uses 22 feet of the ribbon to decorate blankets after she decorates the blanket how many feet of ribbon will remain
Answer:
14 feet
Step-by-step explanation:
There are 3 feet in 1 yard, so 36 feet in 12 yards. The remaining ribbon will be the original amount less the amount used.
36 - 22 = 14 . . . . feet remaining
After decorating the blankets, Olga will have 14 feet of ribbon remaining. The conversion from yards to feet and subtraction calculates this remaining amount accurately.
Calculating Remaining Ribbon
To determine how much ribbon Olga has left after decorating the blankets, we need to perform a couple of conversions and a subtraction.
First, let's convert the total ribbon from yards to feet:
→ 1 yard = 3 feet
→ 12 yards = 12 * 3
= 36 feet
Next, Olga uses 22 feet of ribbon to decorate the blankets:
→ Total ribbon in feet: 36 feet
→ Ribbon used: 22 feet
Now, subtract the amount used from the total:
→ Remaining ribbon = 36 feet - 22 feet
= 14 feet
Olga will have 14 feet of ribbon remaining.
A farmer wants to build a rectangular pen enclosing an area of 100 square feet. He will use wooden fencing on one side, which costs $20 per foot. He will use a chain-link fence on the 3 other sides, which costs $10 per foot. What should the dimensions of the pen be to minimize the cost?
Answer:
The dimensions of the pen that minimize the cost of fencing are:
[tex]x \approx 12.25 \:ft[/tex]
[tex]y \approx 8.17 \:ft[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the width and [tex]y[/tex] the length of the rectangular pen.
We know that the area of this rectangle is going to be [tex]x\cdot y[/tex].The problem tells us that the area is 100 feet, so we get the constraint equation:
[tex]x\cdot y=100[/tex]
The quantity we want to optimize is going to be the cost to make our fence. If we have chain-link on three sides of the pen, say one side of length [tex]y[/tex] and both sides of length [tex]x[/tex], the cost for these sides will be
[tex]10(y+2x)[/tex]
and the remaining side will be fence and hence have cost
[tex]20y[/tex]
Thus we have the objective equation:
[tex]C=10(y+2x)+20y\\C=10y+20x+20y\\C=30y+20x[/tex]
We can solve the constraint equation for one of the variables to get:
[tex]x\cdot y=100\\y=\frac{100}{x}[/tex]
Thus, we get the cost equation in terms of one variable:
[tex]C=30(\frac{100}{x})+20x\\C=\frac{3000}{x}+20x[/tex]
We want to find the dimensions that minimize the cost of the pen, for this reason, we take the derivative of the cost equation and set it equal to zero.
[tex]\frac{d}{dx} C=\frac{d}{dx} (\frac{3000}{x}+20x)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\C'(x)=\frac{d}{dx}\left(\frac{3000}{x}\right)+\frac{d}{dx}\left(20x\right)\\\\C'(x)=-\frac{3000}{x^2}+20[/tex]
[tex]C'(x)=-\frac{3000}{x^2}+20=0\\\\-\frac{3000}{x^2}x^2+20x^2=0\cdot \:x^2\\-3000+20x^2=0\\-3000+20x^2+3000=0+3000\\20x^2=3000\\\frac{20x^2}{20}=\frac{3000}{20}\\x^2=150\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{150},\:x=-\sqrt{150}[/tex]
Because length must always be zero or positive we take [tex]x=\sqrt{150}[/tex] as only value for the width.
To check that this is indeed a value of [tex]x[/tex] that gives us a minimum, we need to take the second derivative of our cost function.
[tex]\frac{d}{dx} C'(x)=\frac{d}{dx} (-\frac{3000}{x^2}+20)\\\\C''(x)=-\frac{d}{dx}\left(\frac{3000}{x^2}\right)+\frac{d}{dx}\left(20\right)\\\\C''(x)=\frac{6000}{x^3}[/tex]
Because [tex]C''(\sqrt{150})=\frac{6000}{\left(\sqrt{150}\right)^3}=\frac{4\sqrt{6}}{3}[/tex] is greater than zero, [tex]x=\sqrt{150}[/tex] is a minimum.
Now, we need values of both x and y, thus as [tex]y=\frac{100}{x}[/tex], we get
[tex]x=\sqrt{150}=5\sqrt{6}=12.25[/tex]
[tex]y=\frac{100}{\sqrt{150}}=\frac{10\sqrt{6}}{3}\approx 8.17[/tex]
The dimensions of the pen that minimize the cost of fencing are:
[tex]x \approx 12.25 \:ft[/tex]
[tex]y \approx 8.17 \:ft[/tex]
A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.Round your answer to four decimals.If 24 items is chosen at random, what is the probability that their mean length is less than 6.2 inches?
Answer: 0.0047
Step-by-step explanation:
Given : A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.
i.e. [tex]\mu=7.1\text{ inches}[/tex]
[tex]\sigma=17\text{ inches}[/tex]
Sample size : n= 24
Let [tex]\overline{X}[/tex] be the sample mean.
Formula : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Then, the probability that their mean length is less than 6.2 inches will be :-
[tex]P(\overline{x}<6.2)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{6.2-7.1}{\dfrac{1.7}{\sqrt{24}}})\\\\\approx P(z<-2.6)\\\\=1-P(z<2.6)\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=1-0.9953=0.0047\ \ \ [ \text{Using z-value table}][/tex]
hence,. the required probability = 0.0047
Answer:
0.0047
step-by-step explanation