Answer:
a) [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] or [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex], b) The magnitude of segment PQ is approximately 11.489, c) The two unit vectors associated to PQ are, respectively: [tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
Step-by-step explanation:
a) The vectorial form of segment PQ is determined as follows:
[tex]\overrightarrow {PQ} = \vec Q - \vec P[/tex]
Where [tex]\vec Q[/tex] and [tex]\vec P[/tex] are the respective locations of points Q and P with respect to origin. If [tex]\vec Q = (13,13,3)[/tex] and [tex]\vec P = (5,5,1)[/tex], then:
[tex]\overrightarrow{PQ} = (13,13,3)-(5,5,1)[/tex]
[tex]\overrightarrow {PQ} = (13-5, 13-5, 3 - 1)[/tex]
[tex]\overrightarrow{PQ} = (8,8, 2)[/tex]
Another form of the previous solution is [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex].
b) The magnitude of the segment PQ is determined with the help of Pythagorean Theorem in terms of rectangular components:
[tex]\|\overrightarrow{PQ}\| =\sqrt{PQ_{x}^{2}+PQ_{y}^{2}+PQ_{z}^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\| = \sqrt{8^{2}+8^{2}+2^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex]
The magnitude of segment PQ is approximately 11.489.
c) There are two unit vectors associated to PQ, one parallel and another antiparallel. That is:
[tex]\vec v_{1} = \vec u_{PQ}[/tex] (parallel) and [tex]\vec v_{2} = -\vec u_{PQ}[/tex] (antiparallel)
The unit vector is defined by the following equation:
[tex]\vec u_{PQ} = \frac{\overrightarrow{PQ}}{\|\overrightarrow{PQ}\|}[/tex]
Given that [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] and [tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex], the unit vector is:
[tex]\vec u_{PQ} = \frac{(8,8,2)}{11.489}[/tex]
[tex]\vec u_{PQ} = \left(\frac{8}{11.489},\frac{8}{11,489},\frac{2}{11.489} \right)[/tex]
[tex]\vec u_{PQ} = \left(0.696, 0.696,0.174\right)[/tex]
The two unit vectors associated to PQ are, respectively:
[tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
The researcher is interested to know if policy A (new) is more effective than policy B (old). Frame the hypothesis and describe what each error would represent in terms of reality and conclusion.
Answer:
Null hypothesis: Policy B remains more effective than policy A.
Alternate hypothesis: Policy A is more effective than policy B.
Step-by-step explanation:
Remember, a hypothesis is a usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.
We have two types of hypothesis errors:
1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.
That is, rejecting the assumption that policy B remains more effective than policy A when it is actually true.
2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is actually false.
Find the value of x.
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
given that sin x equals to a over b then what is tan x
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
a car is driving at a speed of 40mi/h.what is the speed of the car in feet per minute
Answer:
[tex]\boxed{3520\ ft/min}[/tex]
Step-by-step explanation:
1 miles per hour = 88 feet per minute
Multiplying both sides by 40
40 miles per hour = 88*40 ft/min
40 mi./hr = 3520 ft/min
Answer:
3520 feet/min
Step-by-step explanation:
the speed of the car in feet per minute:
first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)
(40*5280)/1*60=3520 feet/min
find the value of the variable and GH if H is between G and I. GI=5b+2,HI=4b-5, HI=3
Answer:
GH = 9 units
Step-by-step explanation:
Given HI = 4b - 5 and HI 3, then
4b - 5 = 3 ( add 5 to both sides )
4b = 8 ( divide both sides by 4 )
b = 2
Thus
GI = 5b + 2 = 5(2) + 2 = 10 + 2 = 12
GH = GI - HI = 12 - 3 = 9
Susan purchased 9/10 of a pound of shrimp for a dinner party. Her plan is to serve 1/6 of a pound of shrimp to herself and each guest. Including herself, how many people can Susan serve at her dinner party? (Remember that you can't have a fraction of a person.)
Answer:
Susan and 4 quests
5 people
Step-by-step explanation:
Take 9/10 and divide by 1/6
9/10 ÷1/6
Copy dot flip
9/10 * 6/1
54/10
50/10 + 4/10
5 4/10
We can only serve whole numbers
5 people
Susan and 4 quests
A cell phone company offers a plan that costs $35 per month plus an additional cost of $0.08 per text message.
Write an equation to represent this problem.
Answer:
C = 35 + 0.08t
Step-by-step explanation:
The equation is:
35 + 0.08t = C
C = Cost by month
t = cost for each additional message
-3 raised to 2 + -3 raised to 2 =
Answer:
Step-by-step explanation:
(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)
= 9 + 9
= 18
Answer:
18
Step-by-step explanation:
Solve the equation for x.
Answer:
x = 27
Step-by-step explanation:
2/3x - 1/9x + 5 = 20
Subtract 5 from each side
2/3x - 1/9x + 5 -5= 20-5
2/3x - 1/9x = 15
Get a common denominator on the left side
2/3 *3/3 x - 1/9x = 15
6/9x - 1/9x = 15
5/9 x = 15
Multiply each side by 9/5
9/5 * 5/9x = 15 * 9/5
x = 15/5 *9
x = 3*9
x = 27
Answer:
x=27
Step-by-step explanation:
2/3 x -1/9 x+5=20
2/3x -1/9 x=20-5 common denominator
(6x-1x)/9=15 multiply each side by 9
(5x)=135
5x=135
x=135/5=27
x=27
Evaluate 7m + 2n - 8p/n for m = –4, n = 2, and p = 1.5.
Answer:
-30
Step-by-step explanation:
7m + 2n - 8p/n
Let m = –4, n = 2, and p = 1.5
7(-4) + 2 ( 2) -8*(1.5)/2
-28 + 4 - 4*1.5
-28+ 4 - 6
-30
Answer:
-30
Step-by-step explanation:
Hey there!
Well given,
m = -4
n = 2
p = 1.5
We need to plug those number into,
7m + 2n - 8p/n
7(-4) + 2(2) - 8(1.5)/(2)
-28 + 4 - 12/2
-28 + 4 - 6
-24 - 6
-30
Hope this helps :)
What is the slope of line m?
Answer:
2.
Step-by-step explanation:
The slope is calculated by doing rise over run.
The rise is: 6 - 0 = 6.
The run is: 0 - (-3) = 0 + 3 = 3.
6 / 3 = 2 / 1 = 2.
Hope this helps!
Find the angle measures given the figure is a rhombus.
Answer:
1 = 90°, 2 = 66°
Step-by-step explanation:
Since the diagonals of a rhombus are perpendicular, ∠1 = 90°. Using the Exterior Angles Theorem (exterior angle = sum of remote interior angles, we see that ∠2 = 90 - 24 = 66°.
Stephanie casts a shadow of 1.2 m and she is 1.8 m tall. A wind turbine casts a shadow of 10m at the same time that Stephanie measured her shadow. Draw a diagram of this situation
and then calculate how tall the wind turbine is.
Answer:
see below for a diagram15 mStep-by-step explanation:
Stephanie is 1.8/1.2 = 1.5 times as tall as her shadow is long. We expect the same is true of the wind turbine.
The wind turbine's shadow is 10 m long, so its height is 1.5·(10 m) = 15 m.
The wind turbine is 15 m tall.
this is 69 points if you answer please help
Answer:
see below
Step-by-step explanation:
Angle C is equal to the 1/2 the difference of the two arcs
C = 1/2 ( large DC - small DC)
Large DC = ( 360 - 5x - 2) sum of a circle is 360 degrees
Small DC = 5x-2 the central angle is equal to the intercepted arc
C = 1/2 ( 360 - 5x-2 - ( 5x -2)) Angle Formed by Two Intersecting Chords
C = 1/2 ( 360 - 2 ( 5x-2))
Distributing the 1/2
C = 180 - (5x-2)
Replacing the C with 2x+7
2x+7 = 180 - (5x-2)
Add 5x-2 to each side
2x+7 +5x-2 = 180
Antonio is correct
Combine like terms
7x +5 = 180
7x = 175
Divide by 7
x =25
Then solve for A = 5x-2
A = 5*25-2
= 125-2
= 123
[4 + (3 – 1)]3 = ? A. 12 B. 32 C. 64 D. 128 E. 216
Answer:
18
Step-by-step explanation:
Answer:
18.
Step-by-step explanation:
[4 + (3 - 1)] * 3
= (4 + 2) * 3
= 6 * 3
= 18
Hope this helps!
Determine the value of x.
Answer:
B. 6sqrt(2).
Step-by-step explanation:
Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.
In this case, x = 6.
So, the hypotenuse is B. 6sqrt(2).
Hope this helps!
If I mix 5 gallons of p% boric acid with 5 gallons of water, what is the concentration of the mixture?
Answer: The concentration of the mixture is 0.5 p % .
Step-by-step explanation:
Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.
Amount of boric acid = p% of 5 gallons
[tex]=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}[/tex]
Total solution : 5 +5 = 10 gallons
then, the concentration of the mixture = [tex]\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100[/tex]
[tex]=\dfrac{0.05p}{10}\times100\\\\=0.5p[/tex]
Hence, the concentration of the mixture is 0.5 p % .
Answer:
0.5p% is the answer
The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? Consider as significant any result that differs from the mean by at least 2 standard deviations. That is, significant values are either less than or equal to muminus2sigma or greater than or equal to muplus2sigma.
Answer:
Yes, it would be statistically significant
Step-by-step explanation:
The information given are;
The percentage of jawbreakers it produces that weigh more than 0.4 ounces = 60%
Number of jawbreakers in the sample, n = 800
The mean proportion of jawbreakers that weigh more than 0.4 = 60% = 0.6 = [tex]\mu _ {\hat p}[/tex] =p
The formula for the standard deviation of a proportion is [tex]\sigma _{\hat p} =\sqrt{\dfrac{p(1-p)}{n} }[/tex]
Solving for the standard deviation gives;
[tex]\sigma _{\hat p} =\sqrt{\dfrac{0.6 \cdot (1-0.6)}{800} } = 0.0173[/tex]
Given that the mean proportion is 0.6, the expected value of jawbreakers that weigh more than 0.4 in the sample of 800 = 800*0.6 = 480
For statistical significance the difference from the mean = 2×[tex]\sigma _{\hat p}[/tex] = 2*0.0173 = 0.0346 the equivalent number of Jaw breakers = 800*0.0346 = 27.7
The z-score of 494 jawbreakers is given as follows;
[tex]Z=\dfrac{x-\mu _{\hat p} }{\sigma _{\hat p} }[/tex]
[tex]Z=\dfrac{494-480 }{0.0173 } = 230.94[/tex]
Therefore, the z-score more than 2 ×[tex]\sigma _{\hat p}[/tex] which is significant.
Answer:
Step-by-step explanation:
min 452, max 507, so 494 is not unusual.
someone plz help !
A town currently has a population of 1,000,000, and the population is increasing 6 percent every year. Write a recursive function in now-next form to predict the population at any year in the future.
Answer:
Y=x(t)(0.06) + x
Y =predicted population
X= population currently
t= number of years
Y= 60000(t) + 1000000
Step-by-step explanation:
Let the current population be x
X= 1000000
The rate of increase= 6% each year
Let the the predicted population= y
If the population is to increase by 6% each year the function predicting the population at the future will be
Y=x(t)(0.06) + x
The only changing value in the above formula is the time.
Y= 1000000(0.06)(t) +1000000
Y= 60000(t) + 1000000
Answer: The actual answer is:
next = now x 1.06, starting at 1,000,000
While watching a circus show, I counted out the number of acrobats and elephants. I counted 40 legs and 15 heads. How many acrobats did I see in the show?
Answer:
y=10 ( number of acrobat)
Step-by-step explanation:
let x be the elephant and y the acrobat
elephant has 4 legs and acrobat 2
4x+2y=40
x+y=15 ⇒x=15-y
substitute for x in the equation:
4(15-y)+2y=40
60-4y+2y=40
-2y=40-60
y=-20/-2
y=10 ( number of acrobat)
number of elephant=15-10=5 elephants
Calculate the amount of paint needed to cover the following door:
Note: You do not paint the window on the inside.
Answer:
Step-by-step explanation:
The door is shape is a combination of a rectangle and a semicircle with a square window.
Area of the door = Area of rectangle + area of a semi circle
Area of a rectangle = Length * Width (LW)
area of a semicircle = πr²/2 where r is the radius of the semi circle.
Given the length of the rectangle = 2m and its width = 1m
Area of rectangle = 2*1 = 2m²
Given the radius of the semicircle = 1/2 m
Area of the semi circle = π(0.5)²/2
= 0.25π/2
= 0.785/2
Area of the semicircle= 0.3925m²
Area of the door = 2+0.3925
Area of the door = 2.3925m²
Since we are not to paint the window, we will subtract the area of the window from the total area.
Area of the window = area of a square = 0.2*0.2
= 0.04m²
Area to be painted = Area of door - Area of the square
Area to be painted = 2.3925m² - 0.04m²
Area to be painted = 2.3535m²
Note that there was no enough information for us to calculate the amount of paint needed but knowing the area of the part to be painted can guide us.
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 200 voters finds that 94 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
Answer:
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Step-by-step explanation:
From the information given :
An exit poll of 200 voters finds that 94 voted for the referendum.
How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
This implies that ;
the Sample size n = 200
the probability p = 0.52
Let X be the random variable
So; the Binomial expression can be represented as:
X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)
Mean [tex]\mu[/tex] = np
Mean [tex]\mu[/tex] = 200 × 0.52
Mean [tex]\mu[/tex] = 104
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]
The standard deviation [tex]\sigma[/tex] = 7.065
However;
P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .
The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5
Now;
x = 94.5
Therefore;
[tex]z = \dfrac{x- \mu}{\sigma}[/tex]
[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]
[tex]z = \dfrac{-9.5}{7.065}[/tex]
z = −1.345
P(X< 94.5) = P(Z < - 1.345)
From the z- table
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)
Answer:
(0, –2)
Step-by-step explanation:
I am assuming that point 'B' is (-5 , 0).
The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].
Apply the rule to point 'B':
[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]
B' should be (0, -2).
Answer:
Guy above me might be right but Im not sure. Im on the cumulative exam on edge.
Step-by-step explanation:
Please help I’m being timed!! A small dairy farm writes a business plan. It includes a graph showing the estimated amount of feed used each day in thousands of pounds, y, compared to the number of years since the farm began operating, x. What does the y-intercept represent? A) the estimated amount of years the farm can afford feed B) the maximum feed per day estimated for the life of the farm C) the estimated amount of feed per day for the start of the farm D) the maximum years the farm needs the originally estimated feed per day
Answer: The Answer is C
Step-by-step explanation: I just took the quiz on ed and this is the correct answer.
Answer: C: the estimated amount of feed per day for the start of the farm
Step-by-step explanation: 100% on quiz
A film distribution manager calculates that 9% of the films released are flops.If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
Answer:
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
Step-by-step explanation:
Given that :
A film distribution manager calculates that 9% of the films released are flops
Let p be the probability for the movies that were released are flops;
[tex]\mu_p = P = 0.9[/tex]
If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%
now; we know that our sample size = 442
the standard deviation of the variance is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]
[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]
[tex]\sigma _p = 0.014[/tex]
So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:
[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]
[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]
[tex]P(|p-P|>0.04)=1 -0.9958[/tex]
[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]
∴
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
Please answer it now in two minutes
Answer:
3.9
Step-by-step explanation:
Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + 1^2 = 4^2
a^2 + 1 = 16
a^2 = 15
a = sqrt(15)
a = 3.9
Answer a = 3.9 yards
Answer:
[tex]\boxed{3.9}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
Apply Pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + 1^2 = 4^2[/tex]
[tex]a^2 + 1 = 16[/tex]
[tex]a^2 = 15[/tex]
[tex]a=\sqrt{15}[/tex]
[tex]a \approx 3.872983[/tex]
On a ski lift, the distance between chairs is inversely proportional to the number of chairs. At a
ski resort, one lift has 80 chairs spaced 16 meters apart. What is the constant of variation.
A.1280 B.5 C.1/5 D.1/1280
Constant of variation = number of chairs/ spacing.
80/16 = 5
The answer is B.5
The coordinates of A, B, and C in the diagram are A (p, 4), B (6, 1 ), and C (9, q). Which equation correctly relates p and q? ↔ ↔ ↔ ↔ Hint: Since AB is perpendicular to BC, the slope of AB × the slope o BC = -1. A. -q − p = 7 B. q − p = 7 C. p − q = 7 D. p + q = 7
Answer:
D. p + q = 7
Step-by-step explanation:
The slope of AB is ...
mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)
The slope of BC is ...
mBC = (q -1)/(9 -6) = (q -1)/3
We want the product of these slopes to be -1:
mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)
-(q-1)/(6 -p) = -1 . . . . cancel factors of 3
q -1 = 6 -p . . . . . multiply by -(6 -p)
q + p = 7 . . . . . matches choice D
Answer:
C p+q=7
Step-by-step explanation:
I did it on plato and it was right
simplify (5 √2 - 1) ^2