Answer: 6 / √26
Step-by-step explanation:
Given that f(x, y, z) = xe^y + ye^z + ze^x
so first we compute the gradient vector at (0, 0, 0)
Δf ( x, y, z ) = [ e^y + ze^x, xe^y + e^z, ye^z + e^x ]
Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]
Now we were also given that V = < 4, 3, -1 >
so ║v║ = √ ( 4² + 3² + (-1)² )
║v║ = √ ( 16 + 9 + 1 )
║v║ = √ 26
It must be noted that "v" is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)
so
⊆ = ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]
therefore by equation D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆
D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]
= ( 1×4 + 1×3 -1×1 ) / √26
= (4 + 3 - 1) / √26
= 6 / √26
A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p).
A. What does it mean to say that f(20)= 10,000 and f firstderivative (20)= -350?
B. Assuming the values in part a, find R first derivative (20).
Answer:
(A) the selling price is $20 per yards, and the expected yards to be sold is 10,000 yards
the derivative f'(20) is negative, which means the fabric producing company will sell 350 fewer yards when selling price is $20 per yard
(B) = R'(20) = $3000
∴the company will get extra $3000 revenue when selling price is $20 per yard
Step-by-step explanation:
A. given that
f(20)= 10,000
f'(20)= -350(first derivative)
the selling price is $20 per yards, and the expected yards to be sold is 10,000 yards
the derivative f'(20) is negative, which means the higher the price, it wil reduce the number of yards to be sold making it 350 fewer yards
(B) R(p) = p f(p)
f(20)= 10,000
f'(20)= -350(first derivative)
R(p) = p f(p)
differentiate with respect to p, using product rule
R'(p) = p f' (p) + f(p) (first derivative)
where p = 20
R'(20) = 20 f' (20) + f(20)
R'(20) = 20(-350) + 10,000
R'(20) = -7000 + 10,000
R'(20) = $3000
∴ the revenue is increasing by $3000 for every selling sold yard and increase in price per yard
(a) The only even prime number is ....
Answer:
2 is the only even prime number
Answer:
2
Step-by-step explanation:
2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.
Suppose that a forester wants to see if the average height of lodgepole pines in Yellowstone is different from the national average of 70 ft. The standard deviation lodgepole pine height is known to be 9.0 ft. The forester decides to measure the height of 19 trees in Yellowstone and use a one-sample z-test with a significance level of 0.01. She constructs the following null and alternative hypotheses, where mu is the mean height of lodgepole pines in Yellowstone.
H_0: mu = 70
H_1: mu notequalto 70
Use software to determine the power of the hypothesis test if the true mean height of lodgepole pines in Yellowstone is 62 ft. You may find one of these software manuals useful. Write your answer in decimal form and round to three decimal places.
Power =
Answer:
You can use your graphing calculator to find the answer.
Go to STAT, then TESTS, and hit "1: Z-Test..."
Make sure it is set to Stats, then for mu0, do 70; for standard deviation, do 9; for mean, you do 62; for sample size, you do 19. For mu, you do not equal to mu0. Then you hit "Calculate".
You then get a z-value (critical value) of -3.874576839, and a p-value of 0.00010685098.
This means that...
We reject the null hypothesis that the average height of lodgepole pines in Yellowstone is 70 feet because p = 0.0001 is less than the significance level of alpha = 0.01. There is sufficient evidence to suggest that the mean height of lodgepole pines in Yellowstone is NOT equal to 70 feet.
Hope this helps!
consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $116. if one-fourth of payments are above $1214,87 what is the mean monthly payment?
Answer:
$1137
Step-by-step explanation:
Solution:-
We will define the random variable as follows:
X: Monthly social security (OASDI) payments
The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).
The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:
X ~ Norm ( μ , σ^2 )
We will define the normal distribution for (OASDI) payments as follows:
X ~ Norm ( μ , 116^2 )
We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:
P ( X > 1214.87 ) = 0.25
We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.
Using standard normal tables, determine the Z-score value corresponding to:
P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75
z-score = 0.675
- Now use the standardizing formula as follows:
[tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]
Answer: The mean value is $1137
Losses covered by a flood insurance policy are uniformly distributed on the interval (0,2). The insurer pays the amount of the loss in excess of a deductible d. The probability that the insurer pays at least 1.20 on a random loss is 0.30. Calculate the probability that the insurer pays at least 1.44 on a random loss.
Answer:
The probability that the insurer pays at least 1.44 on a random loss is 0.18.
Step-by-step explanation:
Let the random variable X represent the losses covered by a flood insurance policy.
The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b\\\\\Rightarrow f_{X}(x)=\frac{1}{2}[/tex]
It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.
That is:
[tex]P(X\geq 1.2+d)=0.30\\[/tex]
⇒
[tex]P(X\geq 1.2+d)=\int\limits^{2}_{1.2+d}{\frac{1}{2}}\, dx[/tex]
[tex]0.30=\frac{2-1.2-d}{2}\\\\0.60=0.80-d\\\\d=0.80-0.60\\\\d=0.20[/tex]
The deductible d is 0.20.
Compute the probability that the insurer pays at least 1.44 on a random loss as follows:
[tex]P(X\geq 1.44+d)=P(X\geq 1.64)[/tex]
[tex]=\int\limits^{2}_{1.64}{\frac{1}{2}}\, dx\\\\=|\frac{x}{2}|\limits^{2}_{1.64}\\\\=\frac{2-1.64}{2}\\\\=0.18[/tex]
Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.
Need Assistance With This
*Please Show Work*
Answer:
a =7.5
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + 10 ^2 = 12.5^2
a^2 + 100 =156.25
Subtract 100 from each side
a^2 = 56.25
Take the square root of each side
sqrt(a^2) = sqrt( 56.25)
a =7.5
A line has a slope of $-\frac{3}{7},$ and its $y$-intercept is $(0,18)$. What is its $x$-intercept?
Answer:
(42, 0)
Step-by-step explanation:
Since we know the slope and y-intercept we can write the equation of the line in slope-intercept form which is y = mx + b; therefore, the equation is y = -3/7x + 18. To find the x-intercept, we just plug in y = 0 which becomes:
0 = -3/7x + 18
-18 = -3/7x
x = 42
[tex]\text{In order to find your x intercept, plug in 0 to y and solve:}\\\\0=-\frac{3}{7}x+18\\\\\text{Subtract 18 from both sides}\\\\-18=-\frac{3}{7}x\\\\\text{Multiply both sides by 7}\\\\-126=-3x\\\\\text{Divide both sides by 3}\\\\42 = x\\\\\text{This means that the x-intercept is (42,0)}\\\\\boxed{\text{x-intercept: (42,0)}}[/tex]
find 10th term of a geometric sequence whose first two terms are 2 and -8. Please answer!!
Answer:
The 10th term is -524,288
Step-by-step explanation:
The general format of a geometric sequence is:
[tex]a_{n} = r*a_{n-1}[/tex]
In which r is the common ratio and [tex]a_{n+1}[/tex] is the previous term.
We can also use the following equation:
[tex]a_{n} = a_{1}*r^{n-1}[/tex]
In which [tex]a_{1}[/tex] is the first term.
The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex]
In this question:
[tex]a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4[/tex]
10th term:
[tex]a_{10} = 2*(-4)^{10-1} = -524288[/tex]
The 10th term is -524,288
For problems 14 and 15, a drain pipe is to be laid between 2 points. One point is 15
feet higher in elevation than the other. The pipe is to slope at an angle of 12° with
the horizontal.
Find the length of the drain pipe. Round to 2 decimal
places.
Answer:
Length of the drain pipe is 72.15 feet.
Step-by-step explanation:
From the figure attached,
A drain pipe is to be laid between two pints P and Q.
Point P is 15 ft higher than the other point Q.
Angle of elevation of point P from point Q is 12°.
Let the length of pipe is l feet.
By applying Sine rule in the given right triangle PRQ,
Sin(∠Q) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
Sin(12) = [tex]\frac{\text{PR}}{\text{PQ}}[/tex]
0.20791 = [tex]\frac{15}{l}[/tex]
[tex]l=\frac{15}{0.20791}[/tex]
[tex]l=72.146[/tex]
l = 72.15 ft
Therefore, length of the drain pipe is 72.15 feet.
Solving exponential functions
Answer:
approximately 30Step-by-step explanation:
[tex]f(x) = 4 {e}^{x} [/tex]
[tex]f(2) = 4 {e}^{2} [/tex]
[tex]f(2) = 4 \times 7.389[/tex]
[tex]f(2) = 29.6[/tex]
( Approximately 30)
Hope this helps..
Good luck on your assignment..
Answer:
approximately 30
Step-by-step explanation:
[tex]f(x)=4e^x[/tex]
Put x as 2 and evaluate.
[tex]f(2)=4e^2[/tex]
[tex]f(2)=4(2.718282)^2[/tex]
[tex]f(2)= 29.556224 \approx 30[/tex]
Perform the indicated operation and write the result in standard form: (-3+2i)(-3-7i)
A. -5+27i
B. 23+15i
C. -5+15i
D. 23-15i
E-5-27I
Answer:
23+15i
Step-by-step explanation:
(-3+2i) (-3-7i)
multiply -3 w (-3+2i) and multiply -7i w (-3+2i)
9-6i+21i-14i^2
combine like terms
9+15i-14i^2
i squared is equal to -1 so
9+15i-(14x-1)
9+14+15i
23+15i
hope this helps :)
A 60-watt light bulb advertises that it will last 1500 hours. The lifetimes of these light bulbs is approximately normally distributed with a mean of 1550 hours and a standard deviation of 57 hours. What proportion of these light bulbs will last less than the advertised time
Answer:
The proportion of these light bulbs that will last less than the advertised time is 18.94% or 0.1894
Step-by-step explanation:
The first thing to do here is to calculate the z-score
Mathematically;
z-score = (x - mean)/SD
= (1500-1550)/57 = -50/57 = -0.88
So the proportion we will need to find is;
P( z < -0.88)
We shall use the standard score table for this and our answer from the table is 0.1894 which is same as 18.94%
An article reported that for a sample of 46 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 163.7.
Required:
a. Calculate and interpret a 9596 (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected.
b. Suppose the investigators had made a rough guess of 175 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?
Answer:
a) CI = ( 148,69 ; 243,31 )
b) n = 189
Step-by-step explanation:
a) If the Confidence Interval is 95 %
α = 5 % or α = 0,05 and α/2 = 0,025
citical value for α/2 = 0,025 is z(c) = 1,96
the MOE ( margin of error is )
1,96* s/√n
1,96* 163,7/ √46
MOE = 47,31
Then CI = 196 ± 47,31
CI = ( 148,69 ; 243,31 )
CI look very wide ( it sems that if sample size was too low )
b) Now if s (sample standard deviation) is 175, and we would like to have only 50 ppm width with Confidence level 95 %, we need to make
MOE = 25 = z(c) * s/√n
25*√n = z(c)* 175
√n = 1,96*175/25
√n = 13,72
n = 188,23
as n is an integer number we make n = 189
Evaluate the function y=1/2(x)-4 for each of the given domain values? PLZ HELP ME
Answer:
c. -13/4.
d. -13/3.
Step-by-step explanation:
c. f(3/2) = (1/2)(3/2) - 4
= 3 / 4 - 4
= 0.75 - 4
= -3.25
= -3 and 1/4
= -13/4.
d. f(-2/3) = (1/2)(-2/3) - 4
= -2/6 - 4
= -1/3 - 4
= -1/3 - 12/3
= -13/3.
Hope this helps!
Isabel works as a tutor for $8 an hour and as a waitress for $9 an hour. This month, she worked a combined total of 93 hours at her two jobs. Let t be the number of hours Isabel worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
We know that t is the number of hours Isabel worked as a tutor, and that she worked for a total of 93 hours. This means that the number of hours she worked as a waitress is 93 - t hours.
Now, for each of the t hours she worked as a tutor, she earned $8, so the total amount Isabel earned from that job is 8t dollars.
For each of the 93 - t hours Isabel worked as a waitress, she earned $9, so the amount she earned from her job as a waitress is 9(93 - t) dollars.
Therefore, the total amount she earned is 8t + 9(93 - t) dollars. This can be simplified to 837 - t dollars.
Select all the correct coordinate pairs and the correct graph. Select the correct zeros and the correct graph of the function below.
Answer:
(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
First graph in top row is the answer.
Step-by-step explanation:
The given function is, f(x) = x⁴ - 4x³ + x² + 6x
For zeros of the given function, f(x) = 0
x⁴ - 4x³ + x² + 6x = 0
x(x³ - 4x² + x + 6) = 0
Therefore, x = 0 is the root.
Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]
= {±1. ±2, ±3, ±6}
By substituting x = -1 in the polynomial,
x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)
= 1 + 4 + 1 - 6
= 0
Therefore, x = -1 is also a root of this function.
For x = 2,
x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)
= 16 - 32 + 4 + 12
= 0
Therefore, x = 2 is a root of the function.
For x = 3,
x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)
= 81 - 108 + 9 + 18
= 0
Therefore, x = 3 is a root of the function.
x = 0, -1, 2, 3 are the roots of the given function.
In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
From these points, first graph in top row is the answer.
Find the area under the standard normal probability distribution between the following pairs of z-scores. a. z=0 and z=3.00 e. z=−3.00 and z=0 b. z=0 and z=1.00 f. z=−1.00 and z=0 c. z=0 and z=2.00 g. z=−1.58 and z=0 d. z=0 and z=0.79 h. z=−0.79 and z=0
Answer:
a. P(0 < z < 3.00) = 0.4987
b. P(0 < z < 1.00) = 0.3414
c. P(0 < z < 2.00) = 0.4773
d. P(0 < z < 0.79) = 0.2852
e. P(-3.00 < z < 0) = 0.4987
f. P(-1.00 < z < 0) = 0.3414
g. P(-1.58 < z < 0) = 0.4429
h. P(-0.79 < z < 0) = 0.2852
Step-by-step explanation:
Find the area under the standard normal probability distribution between the following pairs of z-scores.
a. z=0 and z=3.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 3.00) = 0.9987
Thus;
P(0 < z < 3.00) = 0.9987 - 0.5
P(0 < z < 3.00) = 0.4987
b. b. z=0 and z=1.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 1.00) = 0.8414
Thus;
P(0 < z < 1.00) = 0.8414 - 0.5
P(0 < z < 1.00) = 0.3414
c. z=0 and z=2.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 2.00) = 0.9773
Thus;
P(0 < z < 2.00) = 0.9773 - 0.5
P(0 < z < 2.00) = 0.4773
d. z=0 and z=0.79
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 0.79) = 0.7852
Thus;
P(0 < z < 0.79) = 0.7852- 0.5
P(0 < z < 0.79) = 0.2852
e. z=−3.00 and z=0
From the standard normal distribution tables,
P(Z< -3.00) = 0.0014 and P(Z< 0) = 0.5
Thus;
P(-3.00 < z < 0 ) = 0.5 - 0.0013
P(-3.00 < z < 0) = 0.4987
f. z=−1.00 and z=0
From the standard normal distribution tables,
P(Z< -1.00) = 0.1587 and P(Z< 0) = 0.5
Thus;
P(-1.00 < z < 0 ) = 0.5 - 0.1586
P(-1.00 < z < 0) = 0.3414
g. z=−1.58 and z=0
From the standard normal distribution tables,
P(Z< -1.58) = 0.0571 and P(Z< 0) = 0.5
Thus;
P(-1.58 < z < 0 ) = 0.5 - 0.0571
P(-1.58 < z < 0) = 0.4429
h. z=−0.79 and z=0
From the standard normal distribution tables,
P(Z< -0.79) = 0.2148 and P(Z< 0) = 0.5
Thus;
P(-0.79 < z < 0 ) = 0.5 - 0.2148
P(-0.79 < z < 0) = 0.2852
The formula relating linear velocity v and angular velocity ω for a circle of radius r is______ , where the angular velocity must be measured in radians per unit time.
Answer:
[tex]v=wr[/tex]
Step-by-step explanation:
The formula relating linear velocity v and angular velocity ω for a circle of radius r is
[tex]v=wr------1[/tex]
where v = linear velocity in m/s
w= angular velocity in rad/s
r= radius of curve
Both linear and angular velocity relates to speeds of objects, while linear velocity is to objects that moves, angular velocity is to objects that turns
Please answer this correctly without making mistakes
Answer:
16 km
Step-by-step explanation:
Given:
Distance from Washington to Stamford = distance from Washington to Salem + distance from Salem to Stamford = 10.3 km + 11.9 km = 22.2 km
Distance from Washington to Oakdele = 6.2 km
Required: the difference between the distance from Washington to Stamford and from Washington to Oakdele
Solution:
Distance from Washington to Stamford = 22.2 km
Distance from Washington to Oakdele = 6.2 km
The difference = 22.2 km - 6.2 km = 16 km
Therefore, from Washington, it is 16 km farther to Stamford than to Oakdele.
Find the slope on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Explanation:
Two points on this line are (0,1) and (2,0)
Use the slope formula
m = (y2-y1)/(x2-x1)
m = (0-1)/(2-0)
m = -1/2
The negative slope means the line goes downhill as you move from left to right.
what is the volume of the specker below volume of a cuboid 50cm 0.4m 45cm
Answer:
50*0.4*45=900cm²
Solve the equation.
y + 3 = -y + 9
y= 1
y=3
y = 6
y = 9
Answer: y=3
Step-by-step explanation:
To solve the equation, we want to get the same terms onto the same side and solve.
y+3=-y+9 [add y on both sides]
2y+3=9 [subtract 3 on both sides]
2y=6 [divide 2 on both sides]
y=3
Answer:
y=3
Step-by-step explanation:
Determine by inspection whether the vectors are linearly independent. Justify your answer.
[4 1], [3 9], [1 5], [-1 7]
Choose the correct answer below.
A.The set is linearly dependent because at least one of the vectors is a multiple of another vector.
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
C. The set is linearly dependent because there are four vectors but only two entries in each vector.
D. The set is linearly independent because there are four vectors in the set but only two entries in each vector.
Answer:
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
Step-by-step explanation:
A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
Shawn has a bank account with $4,625. He decides to invest the money at 3.52% interest,
compounded annually. How much will the investment be worth after 9 years? Round to
the nearest dollar.
Answer: The investment will be 6314 after 9 years.
Step-by-step explanation:
Formula to calculate the accumulated amount in t years:
[tex]A=P(1+r)^t[/tex], whereP= principal amount, r= rate of interest ( in decimal)
Given: P = $4,625
r= 3.52% = 0.0352
t= 9 years
Then, the accumulated amount after 9 years would be:
[tex]A=4625(1+0.0352)^9\\\\=4625(1.0352)^9\\\\=4625(1.36527)\approx6314[/tex]
Hence, the investment will be 6314 after 9 years.
10=12-x what would match this equation
Answer:
x=2
Step-by-step explanation:
12-10=2
Answer:
x=2
Step-by-step explanation:
10=12-x
Subtract 12 from each side
10-12 = 12-12-x
-2 =-x
Multiply by -1
2 = x
Find the area under the standard normal curve to the right of z = 2.
Answer:
0.0228
Step-by-step explanation:
A suitable probability calculator (or spreadsheet) can tell you this.
It is about 0.0228.
Suppose that insurance companies did a survey. They randomly surveyed 410 drivers and found that 300 claimed they always buckle up.
We are interested in the population proportion of drivers who claim they always buckle up.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
(i) Enter an exact number as an integer, fraction, or decimal.
x =
(ii) Enter an exact number as an integer, fraction, or decimal.
n =
(iii) Round your answer to four decimal places.
p' =
Which distribution should you use for this problem? (Round your answer to four decimal places.)
P' _ ( , )
Answer:
x = 300
n = 410
p' = 0.7317
[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]
Step-by-step explanation:
From the given information;
the objective is to answer the following:
(i) Enter an exact number as an integer, fraction, or decimal.
Mean x = 300
(ii) Enter an exact number as an integer, fraction, or decimal.
Sample size n = 410
(iii) Round your answer to four decimal places.
Sample proportion p' of the drivers who always claimed they buckle up is :
p' = x/n
p' = 300/410
p' = 0.7317
Which distribution should you use for this problem? (Round your answer to four decimal places.)
P' _ ( , )
The normal distribution is required to be used because we are interested in proportions and the sample size is large.
Let consider X to be the random variable that follows a normal distribution.
X represent the number of people that always claim they buckle up
∴
[tex]P' \sim Normal (\mu = p' , \sigma = \sqrt{\dfrac{p(1-p)}{n}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(1-0.7317)}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(0.2683)}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.19631511}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{4.78817341*10^{-4}})[/tex]
[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]
A ball always bounces to 3/5 of the height from which it is dropped. The ball is dropped from 1.8m and bounces 3 times. How high will it rise from the third bounce?
Answer: 0.388 m
Step-by-step explanation:
Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:
h1 = (3/5)*1.8m = 1.08m
now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:
h2 = (3/5)*1.08m = 0.648m
Now, using the same method as before, the height after the third bounce will be:
h3 = (3/5)*0.648m = 0.388 m
Notice that we can write this relation as:
h(n) = 1.8m*(3/5)^n
where n is the number of bounces.
if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:
h(3) = 1.8m*(3/5)^3 = 0.388 m
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?
Answer:
[tex]B'(x,y) = (0,-2)[/tex]
Step-by-step explanation:
Given
The attached grid
Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]
Required
Determine the coordinates of B'
First, we have to write out the coordinates of B
[tex]B(x,y) = (-5,0)[/tex]
Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]
[tex]B(x,y) = (-5,0)[/tex] becomes
[tex]B'(x,y) = B(x+5,y-2)[/tex]
Substitute -5 for x and 0 for y
[tex]B'(x,y) = (-5+5,0-2)[/tex]
[tex]B'(x,y) = (0,-2)[/tex]