Answer:
The decision is to not reject the null hypothesis.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
The significance level is 0.01.
The sample has a size n=200.
The sample proportion is p=0.54.
[tex]p=X/n=108/200=0.54[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.061)=0.1443[/tex]
As the P-value (0.1443) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.
The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses? 6x + 11 6x − 11 6x2 + 11 6x2 − 11
Answer: 6x² + 11
Step-by-step explanation:
24x³ - 54x² + 44x - 99
= 6x²(4x - 9) + 11(4x - 9)
= (6x² + 11) (4x - 9)
This can be rewritten as: 4x(6x² + 11) - 9(6x² + 11)
This is the answer to your problem.
pls help this is for my little friend thank you
Answer:
Hey there!
3/2 and 3/4 can be written as decimals that terminate.
Hope this helps :)
Answer:
C
Step-by-step explanation:
A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.
3/2=1.5
3/4= 0.75 (It ends after division)
The sum of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
Trust me
Answer:
true
Step-by-step explanation:
URGENT!! The diagram shown below represents the height of a blimp flying over a football stadium. Find the height of the blimp if the angle of elevation at the southern end zone, point A, is 70∘, the angle of elevation from the northern end zone, point B, is 62∘, and the distance between the viewing points of the two end zones is 145 yards. Round your answer to the nearest tenth and do not include units.
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
The height of the blimp over the football stadium = 161.9 yards
Hope this helepd you. Brainliest would be nice!
A motorcycle traveling at a speed of 15 miles/hour comes to a complete stop in 2 seconds when the motorcyclist saw a tiny turtle crossing the road. What is the accel-eration of the motorcycle
answer:
0.25 miles/sec, i hope this helps
Step-by-step explanation:
rename the mixed number as an improper fraction
Answer:
Convert [tex]\frac{2}{3}[/tex] to an improper fraction.
So your answer is [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Hope this helped you!!
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]\frac{11}{3}[/tex]
▹ Step-by-Step Explanation
3 * 3 = 9
9 + 2 = 11
Therefore, the answer is 11/3.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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I need to find for both f(-1) and f(1) it’s
Answer:
f(-1) = -8
f(1) = -12
A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s equals negative 16 t squared plus 256 t. After how many seconds will the ball be 1008 feet from the ground?
Answer:
7 seconds
Step-by-step explanation:
Given the height equation of the motion;
s = -16t^2 + 256t
At s = 1008 ft
The equation becomes;
1008 = -16t^2 + 256t
16t^2 - 256t + 1008 = 0
Solving the quadratic equation for t;
Factorising, we have;
16(t-7)(t-9) = 0
t = 7 or t = 9
When the ball is going up it would reach the given height at time t = 7 seconds.
When it is coming down it would reach the given height at time t = 9 seconds.
Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively. Assume the time of wheel throwing and time of firing are independent random variables.
A) What is the probability that a piece of pottery will befinished within 95 minutes?
B) What is the probability that it will take longer than 110minutes?
Answer:
a) 8.23% probability that a piece of pottery will be finished within 95 minutes
b) 0.28% probability that it will take longer than 110 minutes.
Step-by-step explanation:
Normal distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Two variables:
Means [tex]\mu_{a}, \mu_{b}[/tex]
Standard deviations [tex]\sigma_{a}, \sigma_{b}[/tex]
Sum:
[tex]\mu = \mu_{a} + \mu_{b}[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}[/tex]
In this question:
[tex]\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3[/tex]
So
[tex]\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61[/tex]
A) What is the probability that a piece of pottery will befinished within 95 minutes?
This is the pvalue of Z when X = 95.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{95 - 100}{3.61}[/tex]
[tex]Z = -1.39[/tex]
[tex]Z = -1.39[/tex] has a pvalue of 0.0823
8.23% probability that a piece of pottery will befinished within 95 minutes.
B) What is the probability that it will take longer than 110 minutes?
This is 1 subtracted by the pvalue of Z when X = 110.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{3.61}[/tex]
[tex]Z = 2.77[/tex]
[tex]Z = 2.77[/tex] has a pvalue of 0.9972
1 - 0.9972 = 0.0028
0.28% probability that it will take longer than 110 minutes.
toilet rolls come in packs of 4 and 9
the 4 packed price $2.04
and the 9 packed is priced at $4.68
Answer: 2.04÷ 4= 0.51
4.68÷9= 0.52
4 pack is better value by 0.01
the sum of the first 20 terms of an A.P is identical to the sum of the first 22 term.If the common difference is -2; find the first terms
Answer:
First term a = 41
Step-by-step explanation:
Arithmetic Progression:
Common differences d = -2
[tex]S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\[/tex]
= 10*(2a - 38)
= 10*2a - 10*38
=20a - 380
[tex]S_{22}=\frac{22}{2}(2a+21*[-2])\\\\[/tex]
= 11 (2a -42)
=11*2a - 11*42
= 22a - 462
[tex]S_{22}=S_{20}\\\\[/tex]
22a - 462 = 20a - 380
22a = 20a - 380 + 462
22a = 20a + 82
22a - 20a = 82
2a = 82
a = 82/2
a = 41
First term a = 41
he data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Answer:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 190.82ºF
B. It is unrealistically high.
Step-by-step explanation:
Hello!
*Full text*
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of .05. What is wrong with this predicted value?
Chirps in 1 min. 929 854 771 1004 1201 1027
Temperature (F) 81.3 77.3 64.8 80.3 92.2 80.9
What is the regression equation?
^y= _____ + _____
(Round the x-coefficient to four decimal places as needed. Round the constant to two decimals as needed)
What is the predicted value? ^y= _____ (Round to one decimal places as needed)
What is wrong with this predicted value?
A. The first variable should have been the dependent variable
B. It is unrealistically high.
C. It is only an approximation
D. Nothing is wrong with this value
To calculate the regression equation you have to estimate the slope and the y-intercept.
^Y= a + bX
Estimate of the slope:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
n= 6
∑X= 5786 ∑X²= 5691944 [tex]\frac{}{X}[/tex]= 964.33
∑Y= 476.80 ∑Y²= 38277.76 [tex]\frac{}{Y}[/tex]= 79.47
∑XY= 465940.4
[tex]b= \frac{465940.4-\frac{5786*476.80}{6} }{5691944-\frac{(5786)^2}{6} }= 0.0547[/tex]
Estimate of the Y-intercept:
[tex]a= \frac{}{Y} -b*\frac{}{X}[/tex]
[tex]a= 79.47 -0.0547*964.33= 26.696= 26.72[/tex]
The estimated regression equation is:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 26.72 + 0.0547*3000= 190.82ºF
At the rate of 3000 chirps per minute it is expected a temperature of 190.82ºF
As you can see it is unrealistic to think that the chirping rate of bugs will have any effect over the temperature. For what is known about bugs, they tend to be more active to higher temperatures.
Considering the value obtained, as it is incredible high, if this regression was correct, every time the chirping rate of bugs increases, the ambient temperature would rise to levels incompatible with life.
I hope this helps!
which linear is represented by the graph?
A baseball card collector buys and opens 360 packs of 1989 Fleer baseball cards. He is told that there is a 2.3% chance of anyone pack containing the coveted Billy Ripken error card. Find the mean and standard deviation of the random variable "number of Billy Ripken error cards ound", where n-360
Answer:
Mean: 8.28
Standard deviation: 2.84
Step-by-step explanation:
This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).
Then, the mean and standard deviation are calculate as for the binomial distribution:
[tex]\mu=np=360\cdot 0.023=8.28\\\\\sigma=\sqrt{np(1-p)}=\sqrt{360\cdot 0.023\cdot 0.977}=\sqrt{8.08956}\approx2.84[/tex]
Brainliest to whoever gets this correct True or false: f(x) is a function.
Answer:
f(x) is not a function meaning this is false.
Step-by-step explanation:
One input, can only have one output. In this case 5 has two outputs, 1 and 3. This statement is false.
Hope this helped! :)
___________is an expected error based only on the observations limited to a sample taken from a population
1. Sampling error
2. Survey error
3. Coverage error
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▹ Answer
1. Sampling error
▹ Step-by-Step Explanation
A sampling error is an error in statistics. This means that not the whole population is given a chance to be sampled, which results in this error.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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What is the area , rounded to nearest hundredth?
Answer:
57
Step-by-step explanation:
Area of rectangle:
4 x 12
=48
Area of left triangle:
2 x 3 / 2
=3
Area of right triangle:
6 x 2 / 2
=6
Total Area:
48 + 3 + 6 = 57
Answer: 100
Step-by-step explanation: 4 * 12 = 48 6 * 2 / 0.5 = 24 3 * 2 / 0.5 = 12
48+24+12=84 84 to the nearest hundred is 100.
Look at this expression, and complete the statement 3x+2(x+2)+4
the answer is 3y+2x+8
select the option for "?" that continues the pattern in each question
3,-6, 12, 4, 20
13
14
6
16
Answer:
The next number in the sequence is: 13
Step-by-step explanation:
So we start with 3, then the pattern is:
subtract 9, add 18, subtract 8, add 16, subtract 7, add 14...
If we apply this to the pattern we can see that it works. You should be able to continue the pattern if needed.
Every new computer costs $702.37 from a local store. The nearby school has a policy that every 3 children must have at least 1 computer. If each class has 24 children, how much money should the school spend on computers if there is 17 classes?
Division is one of the four fundamental arithmetic operations. The amount of money the school needs to spend on computers is $95,522.32.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The number of students in a class is 24, while the number of classes is 17. Therefore, the number of students in the classes should be,
[tex]\text{Total number of students} = 24 \times 17 = 408[/tex]
Now, since, there should be a computer for every 3 students, therefore, the number of computers that will be needed are,
[tex]\text{Number of computer} = \dfrac{\text{Number of students}}{3} = \dfrac{408}{3} = 136[/tex]
The cost of a single computer is $702.37, therefore, the cost of 136 computers will be,
[tex]\rm Total\ cost= (\text{Cost of a single computer}) \times 136\\\\ Total\ cost= (\$702.37) \times 136\\\\ Total\ cost= \$95,522.32[/tex]
Hence, the amount of money the school needs to spend on computers is $95,522.32.
Learn more about Division:
https://brainly.com/question/369266
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3. A strip of wood 78 inches long is to be cut into pieces 3 3la inches long. How many pieces can be cut?
A. 21
B. 12
C. 26
D.20
Answer:
Option D (20) is the right answer.
Step-by-step explanation:
The given values are:
Length of wood,
= 78 inches
Wood pieces,
= [tex]3\frac{3}{4} \ inches[/tex]
On converting this in proper fraction, we get
= [tex]3\frac{3}{4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3.75 \ inches[/tex]
Now,
On dividing "78" from "3.78", we get
= [tex]\frac{78}{3.75}[/tex]
= [tex]20.8 \ pieces[/tex]
So we got "20 pieces".
Which lines are parallel? Justify your answer.
A. Lines a and b are pa because their corresponding angles are congruent.
B. Lines a and b are parallel because their same side exterior angles are congruent.
C. Lines e and f are parallel because their corresponding angles are congruent.
D. Lines e and f are parallel because their same side exterior angles are supplementary.
Answer:
A. Lines a and b are pa because their corresponding angles are congruent.
Step-by-step explanation:
The corresponding angles are both 110 degrees.
Given rectangles ABCD and A'B'C'D, describe the transformation that takes place from ABCD to A'B'C'D'
Answer:
A 90° clockwise rotation about the origin and a translation of 7 units down.Step-by-step explanation:
First of all, we need to define the image and pre-image.
The pre-image is the rectangle ABCD, before the transformation. The image is the rectangle A'B'C'D', after the transformation.Second, let's write down the coordinates of each rectangle.
ABCD coordinates:
A(-6,5)
B(-1,5)
C(-1,1)
D(-6,1)
A'B'C'D' coordinates:
A'(5,-1)
B'(5,-6)
C'(1,-6)
D'(1,-1)
The first rule we need to apply is the 90° clockwise rotation which is
[tex](x,y) \implies (y,-x)[/tex]
Which gives us (5,6), (5,1), (1,1), (1,6).
Then, we use the 7 units-down rule
[tex](x,y) \implies (x,y-7)[/tex]
Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).
Therefore, the right answer is the third choice.
Answer:
A 90° clockwise rotation about the origin and a translation of 7 units down.
What is the solution to the following equation?
X/3 - 14 = -2
Answer:
x = 36
Step-by-step explanation:
x/3 - 14 = -2
x - 42 = -6
x = -6 + 42
x = 36
Hope this helps! :)
Answer:
x= 36
Step-by-step explanation:
X/3 - 14 = -2
Add 14 to each side
X/3 - 14+14 = -2+14
x/3 = 12
Multiply each side by 3
x/3 * 3 = 12*3
x = 36
What is the solution to the inequality below?
x < 5
A. x< 25 or x>-25
B. x < 25 or x>0
O C. x< 25 and x > 0
O D. x < 25 and x>-25
Answer:
C. x < 25 and x ≥ 0
Step-by-step explanation:
Fastest and easiest way to do this is to graph the inequality and find out the lines.
A nursing student is planning his schedule for next quarter. He needs to take three courses and one must be statistics. For his other courses, he can choose one of two science classes and one of three social sciences classes. What is the probability that his social sciences class is not Economics?
Answer: 0.66
Step-by-step explanation:
He must choose 2 courses.
The options are:
one of two science classes
one of three social sciences classes.
For the first class selection we do not have any restriction, so that selection can be ignored.
Now, we can assume that one of the 3 social sciences is economics, so we have 2 classes that are not economics.
Then, the probability that he does not select economics (if the selections are at random) is equal to the number of classes that are not economics divided the total number of classes:
p = 2/3 = 0.66
Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
Weekly Usage
(hours) Annual Maintenance
Expense ($100s)
13 17.0
10 22.0
20 30.0
28 37.0
32 47.0
17 30.5
24 32.5
31 39.0
40 51.5
38
40.0
(a) Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage. What is the estimated regression model?
Let x represent the number of hours of weekly usage.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
(b) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(c) How much of the variation in the sample values of annual maintenance cost does the model you estimated in part (b) explain?
If required, round your answer to two decimal places.
(d) If the maintenance contract costs $3000 per year, would you recommend purchasing it? Explain.
Answer:
Step-by-step explanation:
Hello!
The given data corresponds to the variables
Y: Annual Maintenance Expense ($100s)
X: Weekly Usage (hours)
n= 10
∑X= 253; ∑X²= 7347; [tex]\frac{}{X}[/tex]= ∑X/n= 253/10= 25.3 Hours
∑Y= 346.50; ∑Y²= 13010.75; [tex]\frac{}{Y}[/tex]= ∑Y/n= 346.50/10= 34.65 $100s
∑XY= 9668.5
a)
To estimate the slope and y-intercept you have to apply the following formulas:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95[/tex]
[tex]a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53[/tex]
^Y= a + bX
^Y= 10.53 + 0.95X
b)
H₀: β = 0
H₁: β ≠ 0
α:0.05
[tex]F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}[/tex]
F= 47.62
p-value: 0.0001
To decide using the p-value you have to compare it against the level of significance:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.
c)
The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:
[tex]R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86[/tex]
This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X
d)
Without usage, you'd expect the annual maintenance expense to be $1053
If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553
If used 1000 hours weekly the expected maintenance expense will be $96053
It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.
how do you graph y=–7/3x+2. PLEASE HELP ME
Graph the line using the slope and y-intercept, or two points.
Slope: -7/3
y-intercept: 2
Please mark me as brainliest if possible. Stay safe and God bless you!!
<3
- Eli
Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6
The tangent vector to r(t) at any t in the domain is
[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]
At t = π/6, the tanget vector is
[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]
To get the unit tangent, normalize this vector by dividing it by its magnitude:
[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]
So the unit tangent at the given point is
[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]
Applying derivatives, the tangent vector of unit length at the point given is:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
The vector function is:
[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]
The tangent vector is it's derivative, which is given by:
[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]
At point [tex]t = \frac{\pi}{6}[/tex], we have that:
[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]
The norm of the vector is:
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]
The unit vector is given by each component divided by the norm, thus:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
A similar problem is given at https://brainly.com/question/20733439
Which of the following illustrates the truth value of the following mathematical statements?
6 + 3 = 9, and 5.5 = 20
Answer: 6 + 3 = 9
Step-by-step explanation:
5.5 does not equal to 20