Answer:
P(t) = {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)
Step-by-step explanation:
The equation of the tangent line to the given path at the specified value of t is expressed as;
P(t) = f(t0) + f'(t0)(t - t0)
f(t0) = (sin(7t), cos(7t), 2t^9/2)
at t0 = 1;
f(t0) = {sin7(1), cos7(1), 2(1)^9/2}
f(t0) = {sin7, cos7, 2}
f'(t0) = (7cos7t, -7sin7t, 9/2{2t^9/2-1}
f'(t0) = (7cos7t, -7sin7t, 9t^7/2}
If t0 = 1
f'(1) = (7cos7(1), -7sin7(1), 9(1)^7/2)
f'(1) =(7cos7, -7sin7, 9)
Substituting the given function into the tangent equation will give:
P(t) = f(t0) + f'(t0)(t - t0)
P(t)= {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)
The final expression gives the equation of the tangent line to the path.
ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
A positive correlation between two variables X and Y means: If the value of X is above the mean, the
value of Y will be above the mean as well.
A. This is always true.
B. This is sometimes true.
C. This is never true.
Answer: B. This is sometimes true.
Step-by-step explanation:
A positive correlation between 2 variables means that they generally move in the same direction meaning that as one variable rises, the other rises as well and as the other falls, the other falls as well.
However, the correlation can be strong, weak or anything in-between. This means that just because one variable increases by 12 does not mean the other would as well. It could increase by 1 alone and still have a positive correlation albeit a small one.
Therefore, if the value of one variable is above the mean, it doesn't always follow that the other with a positive correlation will as well as they just might not have that strong a correlation.
please help me guys please find the value of 3x°
Answer:
finding the value of x first
2x + 3x + 10 = 180 (linear pair)
5x = 180 - 10
x = 170 / 5
x = 34
3x = 102
A lighthouse casts a
revolving beam of light as far as the pier. What
is the area that the light covers?
Answer:
First, let's find how far away the pier is.
Using the distance formula, we can see that the pier is [tex]\sqrt{58}[/tex] units away.
So, the radius is sqrt 58.
Area = pi (r)^2
So, the area is 182.82 square units.
Let me know if this helps!
We have that The area that the light covers is is mathematically given as
[tex]A=\pi x^2[/tex]
From the Question we are told that
Revolving beam of light as far as the pier
Let distance to pier be x
Generally the revolving beam turns a complete angle of 360
Therefore
Its goes in a circle
The area that the light covers is is mathematically given as
[tex]A=\pi r^2[/tex]
[tex]A=\pi x^2[/tex]
In conclusion
The area that the light covers is is mathematically given as
[tex]A=\pi x^2[/tex]
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Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.
Complete Question
The complete question is shown on the first uploaded image
Answer:
the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
The test statistics is [tex]t = - 1.761[/tex]
The p-value is [tex]p = P(Z < t ) = 0.039119[/tex]
so
[tex]p \ge 0.01[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 122[/tex]
The sample size is n= 38
The sample mean is [tex]\= x = 116 \ feet[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
Generally the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]
[tex]t = - 1.761[/tex]
The p-value is mathematically represented as
[tex]p = P(Z < t )[/tex]
From the z- table
[tex]p = P(Z < t ) = 0.039119[/tex]
So
[tex]p \ge 0.01[/tex]
The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. A random sample of 50 part-time seasonal employees in 2010 had a mean of 38.5 years with a standard deviation of 16 years. Required:a. At the 5 percent level of significance, does this sample show that the average age was different in 2010? b. Which is the right hypotheses to test the statement?c. What are the test statistic and critical value?
Answer:
No the sample does not show that the average age was different in 2010
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The sample mean is [tex]\= x = 38.5[/tex]
The population mean is [tex]\mu = 37[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
The level of significance is [tex]\alpha = 5 \% = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 37[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 37[/tex]
The critical value of the level of significance obtained from the normal distribution table is ([tex]Z_{\alpha } = 1.645[/tex] )
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]
[tex]t = 0.663[/tex]
Now looking at the value t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010
Find the value of x that will make L || M
Answer:
x = 7
Step-by-step explanation:
L and M would be parallel if angle 2x -3 and the angle x + 4 are equal.
Thus, 2x - 3 = x + 4, so that x = 7
The accompanying summary data on total cholesterol level (mmol/l) was obtained from a sample of Asian postmenopausal women who were vegans and another sample of such women who were omnivores.
Diet Sample Size Sample Mean Sample SD
Vegan 85.00 5.20 1.08
Omnivore 91.00 5.65 1.10
Calculate a 99% CI for the difference between the population mean total cholesterol level for vegans and population mean total cholesterol level for omnivores. (Use μvegan−μomnivore). Round to three decimal places.)
Interpret the interval.
a. We are 99% confident that the true average cholesterol level for vegans is less than that of omnivores by an amount within the confidence interval.
b. We are 99% confident that the true average cholesterol level for vegans is greater than that of omnivores by an amount within the confidence interval.
c. We are 99% confident that the true average cholesterol level for vegans is greater than that of omnivores by an amount outside the confidence interval.
d. We cannot draw a conclusion from the given information.
Answer: hey
Step-by-step explanation:
which expression is equivalent to(x²y)³?
Answer:
x^6 y^3
Step-by-step explanation:
(x²y)³
We know that (ab) ^c = a^c * b^c
(x²y)³ = x^2 ^3 * y^3
We know that a^b^c = a^(b*c)
(x²y)³ = x^2 ^3 * y^3 = x^( 2*3) y^3 = x^6 y^3
Which of the following best represents the average rate at which the human hair grows?
Answer:
1/2 inch per month
Step-by-step explanation:
The average rate hair grows is about half an inch per month which is 6 inches per year.
What is the total cost of a $28 pair of jeans if the sales tax is 7.5%?
Answer:
30.10
Step-by-step explanation:
First find the amount of tax
28 * 7.5%
28 * .075
2.10
Add this to the price of the pants
28+2.10 =30.10
who was the first EUROPEAN country that came to Ghana
Answer:
the Portuguese
The History of The Republic of Ghana
The earliest Europeans to set foot on the land were the Portuguese in the 15th century (1471). On their arrival, they found so much gold between the rivers Ankobra and the Volta that they named the area “da Mina”, meaning “The Mine”.
Step-by-step explanation:
This was all I could really find :( Hope this helps! <3
I think it was Portugal
8. Write (2x + 1)(x - 3)(x - 2) in standard form.
2x3 - 9x2 + 6
2x3 - 9x2 + 7x + 6
O
2x3 + 7x - 9x2 + 6
O
7x + 2x3 - 9x2 + 6
Answer:
2x^3 - 9x^2 + 7x + 6
Step-by-step explanation:
(2x + 1)(x - 3)(x - 2)=2x^3 - 9x^2 + 7x + 6
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
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A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 5 days? (2 points)
Answer:
see below
Step-by-step explanation:
Part A
The slope is found by
m = ( y2-y1)/(x2-x1)
= ( 1200-1500)/(4-0)
= -300/4
=-75
Part B
point slope y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y-1200 = -75(x-4)
slope intercept y = mx+b where m is the slope and b is the y intercept
y = -75x + 1500
standard form Ax+By =C
75x + y = 1500
Part C
Change y to g(x) in the slope intercept form
g(x) = -75x + 1500
Part D
Let x = 5
g(5) = -75(5) + 1500
=-375+1500
=1125
Please help with this
Follow the instructions on the image
Answer:
k=3
Step-by-step explanation:
Assuming the centre of dilation is 0,0, we can use the formula (kx,ky) to determine it.
Here,
The co-ordinates of pre-image=(0,1),(-1,-1) & (1,-1)
The co-ordinates of image=(0,3),(-3,-3) & (3,-3)
Now,
(kx,ky)=(0,3)
(k*0,k*1)=(0,3)
Equating,
k=3
You can use the other coordinates to further solidify your answer.
Annie has 3/2 pounds of cookie dough. If she needs 1/16 of a pound of cookie dough to make one cookie, how many cookies can she make
Answer:
[tex]\boxed{\sf 24\ cookies}[/tex]
Step-by-step explanation:
1 cookie = 1/16 of a pound of cookie
If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16
=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]
=> [tex]\frac{3}{2} * 16[/tex]
=> 3*8
=> 24 cookies
Answer:
24 cookies
Step-by-step explanation:
3/2= 1.5 and 1/16= 0.0625
if you divide the amount of dough you have by the amount needed for each cookie you will have 24
1.5/0.0625=24
What is the probability that a student who has no chores has a curfew ?
Answer:
15/22
Step-by-step explanation:
Of the 66 students who have no chores, 45 have a curfew. So the probability is 45/66 = 15/22.
Test the age of the participants (AGE1) against the null hypothesis H0 = 34. Use a one-sample t-test. How would you report the results?
Answer:
t = -1.862, df = 399, p > 0.05
Step-by-step explanation:
The null hypothesis is the statement which is test for its validity. The decision to accept or reject the null hypothesis is based on the test statistics value. In the given question the null hypothesis is H0 = 34. There is one sample t-test for the testing of null hypothesis. The null hypothesis will be same for each type of one sample t-test. The null hypothesis assumes that the difference between the true mean and comparison value is zero.
A cement mixture costs $33 a ton. It is composed of Grade A cement at $36 a ton and Grade B cement at
$24 a ton. How were these two cements mixed?
Use a double angle identity to rewrite the formula r(Θ)=[tex]1/16v^2sin(theta)cos(theta)[/tex]
Answer:
1/32v²sin2θ
Step-by-step explanation:
Given the expression r(theta) = 1/16v²sinθcosθ
According to double angle of trigonometry identity;
Sin2θ = sin(θ+θ)
Sin2θ = sinθcosθ + cosθsinθ
Sin2θ = 2sinθcosθ
sinθcosθ = sin2θ/2 ... **
Substituting equation ** into the question
1/16v²sinθcosθ = 1/16v²(sin2θ/2)
1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)
1/16v²sinθcosθ = 1/32v²sin2θ
Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ
x+3y-Z=0
2x+y+Z=1
3X-y+Z=3
business/multivariable calc question
help needed asap!!!!
I solved and got a max of (8/5,8) at 64/5
Answers:
There is a max value of 81/8 located at (x,y) = (9/8, 9)
=============================================================
Explanation:
Solve the second equation for y
8x+y = 18
y = 18-8x
Plug this into the first equation
f(x,y) = x*y
g(x) = x*(18-8x)
g(x) = 18x-8x^2
This graphs out a parabola that opens downward, and has a max point at the vertex.
If you apply the derivative to this, you get g ' (x) = 18 - 16x
Set this equal to zero and solve for x
g ' (x) = 0
18 - 16x = 0
18 = 16x
16x = 18
x = 18/16
x = 9/8
Use this x value to find y
y = 18 - 8x
y = 18 - 8(9/8)
y = 18 - 9
y = 9
So the max is x*y = (9/8)*9 = 81/8
Or we could say
g(x) = 18x-8x^2
g(9/8) = 18(9/8)-8(9/8)^2
g(9/8) = 81/8
----------------
To summarize,
There is a max value of 81/8 located at (x,y) = (9/8, 9)
When saying "max value of something", we're basically talking about the largest f(x,y) value. Which in this case is the largest x*y value based on the fact that 8x+y = 18.
A practical real world example of a problem like this would be if you wanted to max out a certain rectangular area based on constraints of how much building material you have for the fence.
please help me đáp án của nó là gì help me thanks you very much
Based on this plot, which one of the following statements is not correct? The median room rate is $150 per night. There is one outlier in this data set. The 25th percentile in this data set is $130 per night. The second quartile in the data set is $160 per night.
Answer:
The second quartile in the data set is $130 per night.
Step-by-step explanation:
Quartile is a type of quantile which divides the number of data set into even numbered sub groups. The second quartile is median of data set. This means that 5% of data lies within this point. The middle value between the median and highest value of data set. The second quartile in the data set must be 50% so the statement is not correct.
A school is holding a raffle to raise money to buy new books for the library. The school plans on awarding 18, $200 prizes, 120 $25 prizes and 270 $5 prizes. Is $10 enough to charge per ticket if they only sell 1000 tickets?
Answer:
Yes
Step-by-step explanation:
18 × 200 = 3600
120 × 25 = 3000
270 × 5 = 1350
in total 7950
tickets = 10 × 1000 = 10000
7950 < 10000
(Algebra) PLZ HELP ASAP!
Answer: Rational, integer, whole, natural, real
So basically everything but irrational
====================================================
Explanation:
109 is a rational number because 109 = 109/1. Any rational number is a fraction of two integers. Because of this, it cannot be irrational as "irrational" means "not rational".
An integer is anything that does not have a fractional or decimal part. So it involves the set of positive and negative whole numbers, and zero as well. So we can see that 109 is an integer.
A whole number is very similar to an integer, but we're referring to the set {0, 1, 2, 3, ..} meaning we ignore the negative integers. This makes 109 a whole number as well.
A natural number is from the set {1, 2, 3, ...}. We've kicked 0 out from the set of whole numbers. This is the set of counting numbers. So 109 is also a natural number.
A real number is any number you have encountered so far assuming your teacher has not introduced complex and imaginary numbers yet. Effectively a real number is any number that can be written as decimal. This makes 109 to be a real number.