Answer:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus
Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]
Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]
[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]
Step 2: Integrate Pt. 1
Define vector functions M and N:Step 3: Integrate Pt. 2
We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]
∴ we have evaluated the line integral using Green's Theorem.
---
Learn more about multivariable calculus: https://brainly.com/question/14502499
---
Topic: Multivariable Calculus
Unit: Green's Theorem and Surfaces
Can someone please help me ASAP:(
Answer:
3 =x
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x*x
Divide each side by x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x from each side
3x-3x +3 = 4x-3x
3 =x
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
if it can be assumed that the population is normal, then what is the probability that one man sampled from this population has a weight between 72kg and 88kg
Answer:
The probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.
Step-by-step explanation:
The complete question has the data of mean = 80 kg and standard deviation = 8kg
We have to find the probability between 72 kg and 88 kg
Since it is a normal distribution
(x`- u1 / σ/ √n) < Z >( x`- u2 / σ/ √n)
P (72 <x>88) = P ( 72-80/8/√1) <Z > ( 88-80/8/√1)
= P (-1<Z> 1) = 1- P (Z<1) - P (Z<-1)
= 1- 0.8413- (- 0.8413)= 1- 1.6826= 0.6826
So the probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n
Complete Question
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n=150
Answer:
Normal sampling distribution can not be used
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o : p = 0.015[/tex]
The alternative hypothesis is [tex]H_a : p < 0.015[/tex]
The sample size is n= 150
Generally in order to use normal sampling distribution
The value [tex]np \ge 5[/tex]
So
[tex]np = 0.015 * 150[/tex]
[tex]np = 2.25[/tex]
Given that [tex]np < 5[/tex] normal sampling distribution can not be used
Based on the normal sampling assumption, the product of the sample size and the proportion must be greater than or equal to 5. Hence, since, the condition isn't met, then the normal sampling cannot be used.
Given the Parameters :
Proportion, p = 0.015Sample size, n = 150Test if np ≥ 5 :
(150 × 0.015) = 2.252.25 < 5
Hence, np < 5 ;
Hence, the normal sampling distribution cannot be used.
Learn more : https://brainly.com/question/19338417
. line containing ( −3, 4 ) ( −2, 0)
Answer:
The equation is y= -4x -8
Step-by-step explanation:
The -4 is the slope and the -8 is the y intercept
Answer:
Slope: -4
Line type: Straight and diagonal from left to right going down.
Rate of change: a decrease by 4 for every x vaule
y-intercept is: (0,-8)
x-intercept is: (-2,0)
Step-by-step explanation:
Slope calculations:
y2 - y1 over x2 - x1
0 - 4
-2 - ( -3) or -2 + 3
=
-4/1 =
-4
More slope info on my answer here: https://brainly.com/question/17148844
Hope this helps, and have a good day.
The expression (x - 4)2 is equivalent to which expression
Answer:
8-2x
Step-by-step explanation:
2 distributed over the entire expression equals 8-2x
Answer:
the answer is b
Step-by-step explanation:
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.
Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.
Answer:
(a) The 26th percentile for the number of chocolate chips in a bag is 1185
(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504
Step-by-step explanation:
From the question, we have the following values:
μ =1262 and σ =118
(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.
P( Z<-0.65 )=0.2578 which is approximately 0.26
So for 26th percentile z-score will be -0.65.
Mathematically;
z-score = (x-mean)/SD
-0.65 = (x-1262)/118
-76.7 = x -1262
x = 1262-76.7 = 1185.3
This value is approximately 1,185
(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.
From z-table, we can find the closest probability;
P(-2.05<z<2.05) = 0.96
So we have two x values to get from the individual z-scores
-2.05 = (x-1262)/118
x = 1020(approximately)
For 2.05, we have
2.05 = (x-1262)/118
x = 1262 + 2.05(118) = 1504 (approximately)
Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Answer:
x - 8y - z = 1
Step-by-step explanation:
Data provided according to the question is as follows
f(x,y) = z = ln(x - 8y)
Now the equation for the tangent plane to the surface
For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is
[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]
Now the partial derivatives of f are
[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]
[tex]\\\\=\frac{1}{9-8}[/tex]
= 1
Now
[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]
= -8
So, the tangent equation is
[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]
Now after solving this, the following equation arise
z = x - 9 - 8y + 8
z = x - 8y - 1
Therefore
x - 8y - z = 1
The equation of the tangent plane is [tex]x-8y-z=1[/tex]
Tangent Plane:An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,
[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]
The function is,
[tex]z = ln(x-8y)[/tex]
And the point is (9,1,0)
Now, calculating [tex]f_x,f_y[/tex]
[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]
Now, substituting the given points into the above functions we get,
[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]
So, the equation of the tangent plane is,
[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]
Learn more about the topic tangent plane:
https://brainly.com/question/14850585
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
Help please!!! Tyyyyy
Answer:
D) 60 degree
Step-by-step explanation:
Let's connect the remaining diagonal, which forms a triangle containing angle x.
As a property of regular hexagon, all diagonals are equal.
=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.
Quick! Andrew has to play 15 games in a chess tournament. At some point during the tournament he has won half of the games he has played, he has lost one-third of the games he has played and two have ended in a draw. How many games has Andrew still to play?
[tex]x[/tex] - the number of the games he played
[tex]\dfrac{x}{2}[/tex] - the number of the games he won
[tex]\dfrac{x}{3}[/tex] - the number of the games he lost
[tex]x=\dfrac{x}{2}+\dfrac{x}{3}+2\Big|\cdot6\\6x=3x+2x+12\\x=12[/tex]
[tex]15-12=3[/tex]
so, he has still 3 games to play
The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
A. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?
B. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?
Answer:
A) Maximum error = 170.32 cm³
B)Relative error = 0.0575
Step-by-step explanation:
A) Formula for circumference is: C = 2πr
Differentiating with respect to r, we have;
dC/dr = 2π
r is small, so we can write;
ΔC/Δr = 2π
So, Δr = ΔC/2π
We are told that ΔC = 0.5.
Thus; Δr = 0.5/2π = 0.25/π
Now, formula for Volume of a sphere is;
V(r) = (4/3)πr³
Differentiating with respect to r, we have;
dV/dr = 4πr²
Again, r is small, so we can write;
ΔS/Δr = 4πr²
ΔV = 4πr² × Δr
Rewriting, we have;
ΔV = ((2πr)²/π) × Δr
Since C = 2πr, we now have;
ΔV = (C²/π)Δr
ΔV will be maximum when Δr is maximum
Thus, ΔV = (C²/π) × 0.25/π
C = 82 cm
Thus;
ΔV = (82²/π) × 0.25/π
ΔV = 170.32 cm³
B) Formula for relative error = ΔV/V
Relative error = 170.32/((4/3)πr³)
Relative error = 170.32/((4/3)C³/8π³)
Relative errror = 170.32/((4/3)82³/8π³)
Relative error = 170.32/2963.744
Relative error = 0.0575
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80Help us plazz this is mathematics IGCSE fast as you can
Answer:
Step-by-step explanation:
y varies direcrtly with √(x+5) wich can be expressed mathematically as:
● y = k*√(x+5)
Let's calculate k khowing that y=4 and x=-1
● 4 = k*√(-1+5)
● 4 = k*√(4)
● 4 = k * 2
● k = 4/2
● k = 2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's calculate y khowing that x = 11
● y = k*√(x+5)
● y = 2×√(11+5)
● y = 2× √(16)
● y = 2× 4
● y = 8
Answer:
The value of y is 8.
Step-by-step explanation:
Given that y is directly proportional to √(x+5) so the equation is y = k√(x+5) where k is constant. First, you have to find the value of k with given values :
[tex]y = k \sqrt{x + 5} [/tex]
[tex]let \: x = - 1,y = 4[/tex]
[tex]4 = k \sqrt{ - 1 + 5} [/tex]
[tex]4 = k \sqrt{4} [/tex]
[tex]4 = k(2)[/tex]
[tex]4 \div 2 = k[/tex]
[tex]k = 2[/tex]
So the equation is y = 2√(x+5). In order to find the value of y, you have to substitute x = 11 into the equation :
[tex]y = 2 \sqrt{x + 5} [/tex]
[tex]let \: x = 11[/tex]
[tex]y = 2 \sqrt{11 + 5} [/tex]
[tex]y = 2 \sqrt{16} [/tex]
[tex]y = 2(4)[/tex]
[tex]y = 8[/tex]
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
pt 2 4-7 please helppp
Answer:
f = 16
Step-by-step explanation:
8
8 x 2 = _f_ x
8
f = 16
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------
Answer: f = 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]2 = \frac{f}{8}[/tex]
Multiply both sides by 8.
[tex]2 \times 8 = f[/tex]
Multiply 2 and 8 to get 16.
[tex]16 = f[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]f = 16[/tex]
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8
Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
Find the value of x to the nearest tenth. A) 5 B) 9.2 C) 3.3 D) 2.9
Answer:
B) 9.2
Step-by-step explanation:
tan(57)=x/6 multiply 6 on both sides
6.tan(57)=x use calculator to find answer
9.2 rounded
Answer:9.2 is correct
Step-by-step explanation:
The data set {3, 7, 5, 4, 1} consists of the lengths, in minutes, of a sample of speeches at an awards banquet. Use a formula to find the standard deviation of the sample, and label it with the correct variable.
Answer:
Standard deviation = 2.2360679774998
Step-by-step explanation:
We are asked to find the Standard deviation of a samples of speeches as an awards.
The formula for sample standard deviation is given as:
√[(x - μ)²/N - 1 ]
Step 1
We find the mean (μ)
The mean of the sample =>
= Sum of term/ Number of terms
= (3 + 7 + 5 + 4 + 1)/5
= 20/5
= 4
Step 2
Find the Standard deviation of the sample
√[(x - μ)²/N - 1 ]
N = number of samples or terms = 5
= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]
= √ (1 ² + 3² + -1² + 0² + -3²/4)
= √( 1 + 9 + 1 + 0 + 9/4)
= √20/5 - 1
= √5
= 2.2360679774998
The standard deviation of the sample = 2.2360679774998
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement [Mark 4]
ii. How far west is Musah’s final point from the centre?
Answer:
Inokkohgy8uokokj76899
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
Answer:
3 hours
Step-by-step explanation:
Downstream, the speeds add up:
25 + 4 = 29 km/hIt will take:
87/29= 3 hrsTo ride 87 km.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
Enter your answer as a tri-linear inequality using decimals (not percents).
< p
Answer:
Using Anova for a tri linear probability at ∝= 0.005
Step-by-step explanation:
Here simple probability cannot be used because we want to enter your answer as a tri-linear inequality using decimals (not percents).
So we can use ANOVA
Null hypothesis
H0: µA = µB=µC
all the means are equal
Alternative hypothesis
H1: Not all means are equal.
The significance level is set at α-0.005
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .
The computations are as follows
XA (XA)² XB (XB)² XC (XC)² Total ∑X²
Male 19(361) 4(16) 12(144) 35 521
Female 3(9) 13 (169) 5 (25) 21 203
TotalTj 22 17 17 56 724
T²j (22)(22)
484 289 289 1062
∑X² 370 285 169
Correction Factor = CF = Tj²/n = (56)²/6= 522.67
Total SS ∑∑X²- C. F = 724- 522.67= 201.33
Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33
Within SS = Total SS - Between SS
=201.33- 8.33= 193
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 1 8.33 8.33 8.33/ 48.25= 0.1726
Within
Samples 4 193 48.25
The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328
Calculated value of F = 0.1726
Since it is smaller than 5 % reject H0.
However the decimal probability will be
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
There are total 22 people who get an A but only 19 males who get an A
So the probability that a male gets an A is = 19/22= 0.8636
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
What is the solution to X+9 = 24?
A. x = 33
B. x= 15
C. x= 18
D. x= 9
Answer:
X+9=24
Or,x=24-9
:.x=15
Step-by-step explanation:
Answer:
B. x=15
Step-by-step explanation:
To find the solution to the equation, we must get x by itself on one side of the equation.
[tex]x+9=24[/tex]
9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.
[tex]x+9-9=24-9[/tex]
[tex]x=24-9[/tex]
[tex]x=15[/tex]
Let's check our solution. Plug 15 in for x.
[tex]x+9=24 (x=15)[/tex]
[tex]15+9=24[/tex]
[tex]24=24[/tex]
This checks out, so we know our solution is correct. The answer is B. x=15
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 3y = -9
Answer:
[tex]y = -x - 3[/tex]
Step-by-step explanation:
We are trying to get the equation [tex]3x + 3y = -9[/tex] into the form [tex]y = mx+b[/tex], aka slope-intercept form.
To do this we are trying to isolate y.
[tex]3x + 3y = -9[/tex]
Subtract 3x from both sides:
[tex]3y = -9 - 3x[/tex]
Rearrange the terms:
[tex]3y = -3x - 9[/tex]
Divide both sides by 3:
[tex]y = -x - 3[/tex]
Hope this helped!
A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.
Answer:
The exact distance is [tex]\sqrt{109}[/tex] miles.
The distance is approximately 10.4 miles.
Step-by-step explanation:
It is given that a rectangular city is 3 miles long and 10 miles wide. So,
Length = 3 miles
Width = 10 miles
We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.
Using Pythagoras theorem, the length of diagonal is
[tex]d=\sqrt{l^2+w^2}[/tex]
where, l is length and w is width.
Substitute l=3 and w=10.
[tex]d=\sqrt{(3)^2+(10)^2}[/tex]
[tex]d=\sqrt{9+100}[/tex]
[tex]d=\sqrt{109}[/tex]
The exact distance is [tex]\sqrt{109}[/tex] miles.
Now,
[tex]d=\sqrt{109}[/tex]
[tex]d=10.4403065[/tex]
[tex]d\approx 10.4[/tex]
The distance is approximately 10.4 miles.
what are the like terms of the expression.
3x+8x+y+x+8
Answer:
the like terms are:
3x+8x+x+y+8
12x+y+8
Answer:
The like terms are
3x, 8x, x
Step-by-step explanation:
3x+8x+y+x+8
The like terms are
3x, 8x, x
They are the terms that are in terms of the first power of x
In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
#2. Given the following conditional statement; which answer is
represents the biconditional statement: "If Mr. Anderson is a ninja, then
he can run like Naruto."
Mr. Anderson is a ninja iff he can run like Naruto.
Mr. Anderson can run like Naruto iff he is a ninja.
Mr. Anderson is Naruto iff he can run like a ninja.
Answer:
Mr. Anderson can run like Naruto iff he is a ninja.
Step-by-step explanation:
This is because, in the statement "If Mr. Anderson is a ninja, then he can run like Naruto.", the sub-statement, "he can run like Naruto.", depends on the sub-statement 'If Mr Anderson is a Ninja'. This means that although Mr. Anderson is a Ninja, he can only run like Naruto if and only if he is a Ninja implying that if Mr Anderson is not a Ninja, he cannot run like Naruto.
So, Mr Anderson can run like Naruto iff he is a Ninja is the correct answer
Answer:
1
Step-by-step explanation:
