Answer:
1. constant speed of 6 units per second
2. yes
3. clockwise
4. no it begins from the point ( 0 , 1 )
Step-by-step explanation:
Solution:-
- The position of a particle moving in a path of a unit circle is defined by the following vector equation:-
r ( t ) = sin ( 6t ) i + cos ( 6t ) j
- To determine the speed of the particle in the circular motion we will derivate the position vector ( r ) of the particle with respect to time ( t ) to get the velocity vector:
d r (t ) / dt = v ( t )
v ( t ) = 6*[ cos ( 6t ) i - sin ( 6t ) j ]
- We will determine the speed of the particle by determining the magnitude of the velocity vector v ( t ) as follows:
| v(t) | = [tex]\sqrt{6^2 * cos^2 ( 6t ) + 6^2 * sin^2 ( 6t )}[/tex]
| v(t) | = [tex]\sqrt{36. [cos^2 ( 6t ) + sin^2 ( 6t ) ] }[/tex]
| v(t) | = [tex]\sqrt{36.} \sqrt{1} = 6[/tex]
- The speed | v(t) | remians constant at 6 units per second.
- To determine the acceleration vector a ( t ) we will derivate the velocity vector v ( t ) with respect to time t as follows
d v(t) / dt = a ( t )
a ( t ) = - 36 * [ sin ( 6t ) i + cos ( 6t ) j ]
- To determine whether the two vectors v ( t ) and a ( t ) are orthogonal to each other we will apply the dot product test for orthogonal vectors to be equal to zero as follows:
v(t) . a (t) = -6*36 [ cos ( 6t ) * sin ( 6t ) - sin ( 6t ) * cos ( 6t ) ]
v(t) . a (t) = -6*36 [ 0 ] = 0 ... ( proven )
- The velocity and acceleration vectors are orthogonal at all times t.
- To determine the direction of particle motion we will plug in two consecutive values of t = 0 and t = π / 6 and determine the value of position vector r ( t ):
r ( 0 ) = sin ( 0 ) i + cos ( 0 ) j
r ( 0 ) = 0 i + 1 j
r ( π / 12 ) = sin ( π/2 ) i + cos ( π /2 ) j
r ( π / 12 ) = 1 i + 0 j
- Plot the two points r ( 0 ) and r ( π / 12 ) on a Cartesian coordinate system and join the two with a curve directed from [ 0 i + 1 j ] to [ 1 i + 0 j ]. We see the motion is clockwise and starts from point ( 0 , 1 ) not ( 1 , 0 )
A housing loan corporation states that it sanctions 80% of all housing loans within 7 working days once the verification process is completed. A customer group believes that all housing loans applied to this corporation that are settled within 7 working days is less than 80% of all housing loans. In a sample of 120 housing loan applications, the group found that 92 were settled within 7 working days.
State the null and the alternative hypotheses.
H_0: p = 0.8 vs. H_a: p notequalto 0.8
H_0: p = 0.8 vs. H_a: p > 0.8
H_0: p = 0.8 vs. H_a: p lessthanorequalto 0.8
H_0: p = 0.8 vs. H_a: p greaterthanorequalto 0.8
H_0: p = 0.8 vs. H_a: p < 0.8
Find the point estimate of the population proportion.
0.80
0.23
0.77
0.50
0.20
Calculate the value of the test statistic.
-0.933
0.913
0.933
-0.913
-0.863
Answer:
a)
Answer : d)
Null hypothesis:-H₀ : p =0.8
Alternative Hypothesis :H₁: p < 0.8
b)
Answer : c)0.77
point estimate of the population proportion= 0.77
c)
Answer : e) -0.863
Step-by-step explanation:
step(i):-
Given Population proportion 'p' =80% = 0.80
Given a sample of 120 housing loan applications, the group found that 92 were settled within 7 working days.
Sample proportion or point estimation
[tex]p^{-} = \frac{x}{n} = \frac{92}{120} =0.766[/tex]
Null hypothesis:-H₀ : p =0.8
Alternative Hypothesis :H₁: p < 0.8
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -p}{\sqrt{\frac{p q}{n} } }[/tex]
population proportion p =0.8
q = 1-p = 1-0.8 =0.2
[tex]Z = \frac{0.77 -0.80}{\sqrt{\frac{0.80 x 0.20}{120} } }[/tex]
Z = -0.863
|Z| = | -0.863| = 0.863 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
. A customer group believes that all housing loans applied to this corporation that are settled within 7 working days is equal to the 80% of all housing loans.
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 24 feet high
Answer:
0.0221 feet per minute.
Step-by-step explanation:
[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]
If the Base Diameter = Height of the Cone
The radius of the Cone = h/2
Therefore,
[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]
Rate of Change of the Volume, [tex]\dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]
Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.
[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]
We want to determine how fast is the height of the pile is increasing when the pile is 24 feet high.
We have:
[tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10\\\\$When h=24$ feet$\\\dfrac{3\pi *24^2}{12}\dfrac{dh}{dt}=10\\144\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{144\pi}\\ \dfrac{dh}{dt}=0.0221$ feet per minute[/tex]
When the pile is 24 feet high, the height of the pile is increasing at a rate of 0.0221 feet per minute.
PLZ help I will mark as brainliest
Decode the addition or subtraction problem (Change asterisks to digits, to make the operation correct.) 6*5* − *8*4=2856
Answer:
6750 - 3894 = 2856
Step-by-step explanation:
You have to make use of the arithmetic facts you know.
The least-significant asterisk must be 0, because the sum of 4 and 6 is 10.
The 10s asterisk must be 9,so that the sum 5 + 9 + 1 has a least-significant digit of 5.
The 100s asterisk must be 7, because that is the least-significant digit of the sum 8 + 8 + 1 = 17.
The 1000s asterisk must be 3, so that 2 + 3 + 1 = 6.
(The "1" in each of these sums is the carry from the sum of the digits with the next lower place value.)
So, the subtraction problem is ...
6750 - 3894 = 2856
_____
Comment on the solution method
For the most part, we worked this as an addition problem. The sum of the last two numbers must be equal to the first: 6570 = 3894 +2856. For some of us, addition facts are easier to work with than subtraction facts. The carry/borrow can be less confusing that way.
El precio de un ordenador portátil ha aumentado un 25% y posteriormente fue rebajado un cierto porcentaje.Calcule que porcentaje de descuento habría que aplicar para que quede al precio original de antes del aumento. Porfa responder!!!
Answer:
Se requiere un 20 por ciento de descuento.
Step-by-step explanation:
(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)
Sea [tex]p_{o}[/tex] el precio original del computador portatil, el nuevo precio es:
[tex]p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}[/tex]
[tex]p_{1} = 1.25\cdot p_{o}[/tex]
Si [tex]p_{2} = p_{o}[/tex], entonces el porcentaje requerido para recuperar el precio original es:
[tex]r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%[/tex]
[tex]r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%[/tex]
[tex]r = \left(1-\frac{1}{1.25} \right)\times 100\,\%[/tex]
[tex]r = 20\,\%[/tex]
Se requiere un 20 por ciento de descuento.
Each have four possible answers left parenthesis a,b,c,d right parenthesis, one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find P(CWC), where C denotes a correct answer and W denotes a wrong answer.
b. Beginning with CWC, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list.P(CWC)minussee above P(WCC)equals? 0.046875 P(CCW)equals? 0.046875 (Type exact answers.)
c. Based on the preceding results, what is the probability of getting exactly two correct answers when three guesses aremade?
Answer:
a. P(CWC)=0.046875
b. P(WCC)=0.046875
P(CCW)=0.046875
c. P=0.140625
Step-by-step explanation:
By the rule of multiplication there are 64 forms to answer three questions. This is calculated as:
4 _ * 4 * 4 = 64
1st question 2nd question 3rd question
Because there are 4 options for every question. At the same way, from that 64 options, 3 are CWC and it is calculated as:
1 _ * 3 * 1 = 3
1st question 2nd question 3rd question
Because there is just one answer that is correct for the first question, there are 3 answers wrong for the second question and there are 1 answer correct for the third question.
So, the probability P(CWC) is equal to:
[tex]P(CWC)=\frac{3}{64}=0.046875[/tex]
Then, the complete list of the different possible arrangements of two correct answers and one wrong answer are: CWC, WCC and CCW
Therefore, the probabilities P(WCC) and P(CCW) are calculated as:
[tex]P(WCC)=\frac{3*1*1}{64}=\frac{3}{4}= 0.046875[/tex]
[tex]P(CCW)=\frac{1*1*3}{64}=\frac{3}{4}= 0.046875[/tex]
Finally, the probability of getting exactly two correct answers is the sum of the probabilities calculated before.
[tex]P=P(CWC)+P(WCC)+P(CCW)\\P=0.046875+0.046875+0.046875\\P=0.140625[/tex]
The geometric sequence ; is defined by the formula: a i a 1 =10 a i =a i-1 * 9/10 Find the sum of the first 75 terms in the sequence .
Question:
The geometric sequence ; is defined by the formula: [tex]a_1 =10[/tex] ; [tex]a_i =a_{i-1} * \frac{9}{10}[/tex] Find the sum of the first 75 terms in the sequence .
Answer:
[tex]S_{75} = 99.963001151[/tex]
Step-by-step explanation:
Given
[tex]a_1 =10[/tex]
[tex]a_i =a_{i-1} * \frac{9}{10}[/tex]
Required
Find the sum of 75 terms
Given that the sequence is geometric;
First, the common ratio has to be calculated;
The common ratio is defined as follows;
[tex]r = \frac{a_{i}}{a_{i-1}}[/tex]
Let [tex]i = 2[/tex]
[tex]r = \frac{a_{2}}{a_{2-1}}[/tex]
[tex]r = \frac{a_{2}}{a_{1}}[/tex]
So,
[tex]a_i =a_{i-1} * \frac{9}{10}[/tex] becomes
[tex]a_2 =a_{2-1} * \frac{9}{10}[/tex]
[tex]a_2 =a_{1} * \frac{9}{10}[/tex]
Divide through by [tex]a_1[/tex]
[tex]\frac{a_2}{a_1} =\frac{a_{1} * \frac{9}{10}}{a_1}[/tex]
[tex]\frac{a_2}{a_1} = \frac{9}{10}[/tex]
Recall that [tex]r = \frac{a_{2}}{a_{1}}[/tex]
So, [tex]r = \frac{9}{10}[/tex]
Given that r < 1;
The sum of n terms is calculated as thus;
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
To calculate the sum of the first 75 terms, we have the following parameters
[tex]n = 75\\a = a_1 = 10\\r = \frac{9}{10} = 0.9[/tex]
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex] becomes
[tex]S_{75} = \frac{10(1-0.9^{75})}{1-0.9}[/tex]
[tex]S_{75} = \frac{10(1-0.9^{75})}{0.1}[/tex]
[tex]S_{75} = 100(1-0.9^{75})[/tex]
[tex]S_{75} = 100(1-0.00036998848)[/tex]
[tex]S_{75} = 100(0.99963001151)[/tex]
[tex]S_{75} = 99.963001151[/tex]
What three-digit number with units digit 2 and hundreds digit 4 is divisible by 9?
Answer:
Dear user,
Answer to your query is provided below
A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.
Step-by-step explanation:
Here , It is given that the number is three digit in which units digit is 2 and hundreds digit is 4.
As per rule, the sum of its digits should've divisible by 9. So, Let the unknown digit be X .
Therefore, 2+X+4 =9
This implies, X = 9-2-4 = 3
So, the three digit number will be 432.
Verify - 432/9 = 48
Hence proved
A government agency has 6000 employees. As an alternative to the traditional five-day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The accompanying segmented bar chart is based on the data collected. Which of the following statements is true about work week preferences and age category? A. Preferences appear to be independent of age. B. The distribution of preferences is the same across different age groups. C. A greater percentage of employees who prefer flex hors are in the over 45 age category compared to those who prefer 4-day work week. D. A greater percentage of employees who prefer a 4-day work week are in the over 45 age category compared to those who prefer flax hours.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option D is the correct answer
Step-by-step explanation:
Now looking at the bar chart we see that a greater number of employee over the age of 45 preferred the 4-day work week compared to the number of employee between 30- 45 who preferred to have a flexible work hour and employee below 30 who' s preference are the same for both type of work hours
The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
Answer:
V(r) is the volume of basketball when the radius is r.
Answer:
B. the volume of the basketball when the radius is r
Step-by-step explanation:
I had $5 my mom gave me $10 my dad gave me $30 my aunt and uncle gave me$100 I had another $5 how much do I have
Answer:
150
Step-by-step explanation:
5+10=15
15+30=45
45+100=145
145+5=150
Which of the following graphs represents the equation y=3x+2?
Answer:graph C is the answer because if you put the both values from the graph it satisfies the equation
Answer:
Graph C
Step-by-step explanation:
The given equation is in the form y=mx+b
This is slope-intercept form.
This is where m represents the slope, and b represents the y-intercept.
Therefore, the slope is 3 and the y-intercept is 2.
Let's first name all the equations with a y-intercept of 2.
That would be B and C.
Now, let's find the equation with a slope of 3.
Let's find the slope for B.
The formula for slope is: y1-y2/x1-x2
A point is: (x coordinate, y coordinate)
In the formula,
y1 is the y coordinate of the first point
y2 is the y coordinate of the second point
x1 is the x coordinate of the first point
x2 is the x coordinate of the second point
This said, we can plug our points in.
6-2/2-0
4/2
2
The slope for Graph B is 2, so it is incorrect.
Let's find the slope for Graph C.
2-(-1)/0-(-1)
2+1/0+1
3/1
3
The slope for Graph C is 3, and it has a y-intercept of 2, so Graph C is the correct choice.
y= -x + 1/2+1
- 3x+y=6
Write the expressions "Four times the difference of a number and 1 is equal to six times the sum of the number and three. Find the number
Answer:
4(x - 1) = 6(x + 3)
x = -11
Step-by-step explanation:
x represents “the number” so we would substitute this with a variable.
(I hope this helps! Have a great day AND STAN BTS)
For the function, f(x) = -3x + 5.
If f(x) = -1, what is the value of x?
Answer:
x=2
Step-by-step explanation:
f(x) = -3x + 5.
f(x) =-1
-1 = -3x+5
Subtract 5 from each side
-1 -5 = -3x+5-5
-6 = -3x
Divide each side by -3
-6/-3 = -3x/-3
2 =x
What is the symbol for pi?
Answer:
π
Step-by-step explanation:
What is the square root of -1 ?
Answer:
i
Step-by-step explanation:
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 55 types of sandwiches, and 44 types of chips. How many different value meal packages are possible?
Answer:
159,720
Step-by-step explanation:
Calculation of how many different value meal packages are possible at Ron's Subs :
The meal package at Ron's Subs are:
Drink 66
Sandwich 55
Bag of chips 44
Since we are looking for the how many different value meal packages are possible that means we have to multiply all the three value meal package with each other.
Hence,
Drink 66 ×Sandwich 55 ×Bag of chips 44
=159,720
Therefore 159,720 is the number of different value meal packages that are possible at Ron's Subs
Provide an appropriate response. A 28-year-old man pays $94 for a one-year life insurance policy with coverage of $120,000. If the probability that he will live through the year is 0.9991, what is the expected value for the insurance policy
Answer:
$ 14.08
Step-by-step explanation:
We have that the policy costs $ 94 and with life insurance with coverage of $ 120,000, to calculate the expected value, we must subtract the value of that life insurance multiplied with the probability of dying (complement of the probability of living) and the policy value multiplied by the probability of staying alive) like this:
120000 * (1 - 0.9991) - 94 * 0.9991 = 14.0846
Which means that the expected value of the policy is $ 14.08
Everyday, Jason has a 14-mile round-trip drive to work. He then has to drive his truck on a 296-mile delivery route 5 days a week. How many miles does he drive each day?
Answer:
73.2 miles i am not so sure
Step-by-step explanation:
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. In a certain soccer league, 43% of the 14 teams had won more games than they had lost Choose the correct answer below.
A. Statistic, because the data set of a sample of teams in a league is a sample.
B. Statistic, because the data set of a sample of teams in a league is a population.
C. Parameter, because the data set of all 14 teams is a population.
D. Statistic, because the data set of all 14 teams is a sample.
E. Parameter, because the data set of all 14 teams is a sample.
F. Parameter, because the data set of a sample of teams in a league is a population.
G. Parameter, because the data set of a sample of teams in a league is a sample.
H. Statistic, because the data set of all 14 teams is a population.
Answer:
Step-by-step explanation:
A Parameter is a value that represents a property of a population. This could be the population mean.
A statistic is a value that represents a property of a sample. This could be the sample mean.
In the given scenario, the population is the entire 14 teams. This means that the percentage given is a value representing a property of the population. Therefore, the correct answer is
C. Parameter, because the data set of all 14 teams is a population.
Answer: A Parameter is a value that represents a property of a population. This could be the population mean.A statistic is a value that represents a property of a sample. This could be the sample mean.In the given scenario, the population is the entire 14 teams. This means that the percentage given is a value representing a property of the population. Therefore, the correct answer is C. Parameter, because the data set of all 14 teams is a population.
Step-by-step explanation:
jason went shopping.
he bought a watch and a pair of trainers for a total price of £53.55
this price includes a 15% loyalty discount.
before the discount the trainers were priced at £38.
work out the price before the discount.
Answer:
The total price before discount was £63.
The price of the watch before discount was £25.
Step-by-step explanation:
Let the total original price before discount be x.
The total of £53.55 included a 15% discount. That means he paid only 85% of the original total price before the discount.
85% of x = £53.55
0.85x = 53.55
x = 63
The total before discount was £63.
£63 - £38 = £25
The total price before discount was £63.
The price of the watch before discount was £25.
T(x)=70(.80)*+20 where x is the time in minutes and the T is the temperature in degree celsius . What is the initial temperature of the coffee?
Answer:
The initial temperature of the coffee was 90°C.
Step-by-step explanation:
The function representing the temperature of the coffee after x minutes is:
[tex]T(x)=70\cdot(0.80)^{x}+20[/tex]
T is the temperature in degree Celsius.
The initial temperature of the coffee will be at x = 0.
Compute the value of T (x) at x = 0 as follows:
[tex]T(x)=70\cdot(0.80)^{x}+20[/tex]
[tex]T(0)=70\cdot (0.80)^{0}+20[/tex]
[tex]=70\times 1+20\\=70+20\\=90[/tex]
Thus, the initial temperature of the coffee was 90°C.
An object travels along a horizontal path at a constant rate.the object travels 1/20 of the length of the path in 3/4 second.at that rate,how many seconds does it take the object to travel the entire length of the path?
Answer:
The onject 1/8 of the length of the path 3/4 in second.
Using the ratio and proportion to find the total time does it take the object to travel the entire length of the path as following
Length:time
X:(total time )
Total time x.(3/4)/(1/8x)=(3/4)/(1/8) = 6 seconds
According to the Mortgage Bankers Association, 21% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of seven mortgages was selected. What is the standard deviation of this distribution
Answer:
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
Step-by-step explanation:
For each mortgage, there are only two possible outcomes. Either it is delinquent, or it is not. The probability of a mortgage being delinquent is independent of other mortgages. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
21% of U.S. mortgages were delinquent last year.
This means that [tex]p = 0.21[/tex]
A random sample of seven mortgages was selected.
This means that [tex]n = 7[/tex]
What is the standard deviation of this distribution
[tex]\sqrt{V(X)} = \sqrt{7*0.21*0.79} = 1.08[/tex]
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
If f(x) = 3x + 10 and g(x) = 2x – 4, find (f – g)(x).
Answer:
D
Step-by-step explanation:
Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay
Answer:
$4.20
Step-by-step explanation:
Calculation for the standard deviation of the fare passengers pay of Blue Cab Company:
T = Total amount of the cab fare
Formula for Standard deviation of T will be:
T = σa+bX= bσX.
To convert the rate to dollars per mile from dollars per tenth of a mile, it will be:
b= 3
Hence,
Standard deviation of T is :
3.00(1.4) = $4.20.
What is the final amount if 931 is decreased by 1% followed by a 1% increase?
Give your answer rounded to 2 DP.
Answer:
930.91
Step-by-step explanation:
931 x 99% = 921.69
921.69 x 101% = 930.9069
Answer:
930.91
Step-by-step explanation:
931*99%=921.69
921.69*101=930.91
(80 POINTS) What rule describes a dilation with a scale factor of ½ and the center of dilation at the origin?
Answer:
C
Step-by-step explanation:
(x, y) -> (1/2x, 1/2y)
When you dilate a side, point, etc, you are multiplying the original dimension by the scale factor. That is represented in option C: the original x and y are multiplied by the scale factor, 1/2! Hope that helps! :)
Answer:
C. (x,y) → (1/2x,1/2y)
Step-by-step explanation:
Dialation means to multiply each coordinate by scale factor and in this case it's 1/2
17)Let f(x) = -2x + 5 and g(x) = 9x2 + 4. Find f(8) + g(8) . A)565 B)569 C)564 D)560
Answer:
answer B [tex]\boxed{ \ 569 \ }\\[/tex]
Step-by-step explanation:
f(8)=-2*8+5=-11
g(8)=9*8*8+4=580
f(8)+g(8)= -11+580=569
What is the solution to the equation below? Round your answer to two
decimal places.
In x = 0.2
A. x= 1.22
B. X= 1.58
C. x = -1.61
D. X = -0.70
Answer:
X=1.22
Step-by-step explanation:
I just got the question wrong and it gave me the right answer