At 1pm a Ship sailing South at 18 knots is 40 miles due East of a Boat travelling East at 24 knots. When will the two vessels be closest to each other?
Answers
The two vessels will be closest to each other when the ship is directly south of the boat.
At time t hours, the boat will have traveled 24t miles East, so its position will be (24t,0). The ship will have traveled 18t miles South, so its position will be (40, -18t).
The distance between the two vessels is given by the distance formula:
d = sqrt((40 - 24t)^2 + (-18t)^2)
We want to find the time when this distance is minimized. To do this, we can take the derivative of d with respect to t and set it equal to 0:
d/dt = (1/2)(2(40 - 24t)(-24) + 2(-18t)(-18)) / sqrt((40 - 24t)^2 + (-18t)^2) = 0
Simplifying this equation, we get:
-5760 + 864t + 324t = 0
t = 10/3
So the two vessels will be closest to each other 10/3 hours, or approximately 3.33 hours, after they were first spotted.
At 1 pm, the ship is sailing south at 18 knots, and the boat is traveling east at 24 knots.
To find when the two vessels will be closest to each other, we need to determine the shortest distance between their paths.
Let t be the time (in hours) after 1 pm. The ship's southward distance from its starting point is 18t, while the boat's eastward distance from its starting point is 24t. The initial separation is 40 miles.
Using the Pythagorean theorem, the distance between the two vessels is given by:
D^2 = (18t)^2 + (24t + 40)^2
To minimize D^2, we can differentiate it with respect to t and set the derivative equal to zero:
d(D^2)/dt = 0
Solving this equation for t will give us the time when the two vessels are closest to each other. After solving, we find t ≈ 1.333 hours. So, the closest distance occurs at approximately 1:20 pm (1 hour and 20 minutes after 1 pm).
Visit here to learn more about Pythagorean theorem:
brainly.com/question/21332040
#SPJ11
Related Questions
Steven owns a restaurant that specializes in steakburgers 4 burgers and 3 fries cost $24.50. if a burger costs $5, how much is each order
Answers
Answer:
As we know each burger costs $5
There are 4 burgers
When you do 4×5 you will get 20
Now subtract that 20 from the total cost
24.50-20=4.5
$4.5 is how much it costs for 3 fries
If you're wanting to calculate the number for one thing of fries then divide that 4.5 by 3
4.5/3=1.5
For one thing of fries it will cost $1.5
I hope this helps :)
Calculate the surface area of the following prism
I will give brainliest too
In case you need formula :
Total area of the lateral faces + 2 x base area = perimeter of the base x height + 2 x base area
Answers
Answer:
63sq. meters
Step-by-step explanation:
The Surface area of the pyramid = 2B + ph
Base area B = 1/2 * 2 * 1.5
B = 1 * 1.5
B = 1.5m²
Perimeter of the base = 2 + 1.5 + 2.5
p = 6m
Height of the priscm = 10m
Substitute into the formula;
TSA = 2(1.5) + 6(10)
TSA = 3.0 + 60
TSA = 63sq. meters
Hence the surface area is 63sq. meters
is figure pqrstu a translation, reflection, or rotation? Explain your reasoning
PLEASE HELP ME
Answers
Answer: I'd say reflection
Answer:
It is a reflection
Step-by-step explanation:
In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
find an equation of the tangent line to the curve at the given point. y = ln(x2 − 2x + 1), (2, 0)
Answers
The equation of the tangent line to the curve y = ln(x^2 - 2x + 1) at the point (2, 0) is y = 2x - 4.
First, let's find the derivative of the function
y = ln(x^2 - 2x + 1).
Using the chain rule, the derivative is given by:
dy/dx = (1 / (x^2 - 2x + 1)) * (2x - 2) = (2x - 2) / (x^2 - 2x + 1)
Now, we can find the slope of the tangent line at x = 2 by substituting the x-coordinate of the given point into the derivative:
m = (2(2) - 2) / ((2)^2 - 2(2) + 1) = 2 / 1 = 2
So, the slope of the tangent line at the point (2, 0) is 2.
Next, we can use the point-slope form of the equation of a line to find the equation of the tangent line.
Given the point (2, 0) and the slope m = 2, the equation of the tangent line is:
y - 0 = 2(x - 2)
Simplifying this equation gives us the equation of the tangent line:
y = 2x - 4
Therefore, the equation of the tangent line to the curve y = ln(x^2 - 2x + 1) at the point (2, 0) is y = 2x - 4.
To learn more about chain rule click here: brainly.com/question/31585086
#SPJ11
Use this information for questions
5 and 6.
It costs $7.50 per person to ice skate at Chea
Skate Rink. Five friends went to Cheap Skat
for the afternoon.
5. Which equation can be used to find th
total cost?
Answers
Answer:
7.5x = total cost
As the cost is 7.5 dollars for each person, multiple the cost by the amount of people for the total cost of the whole party.
for an experiment involving 3 levels of factor a and 3 levels of factor b with a sample of n = 8 in each treatment condition, what are the df values for the f-ratio for the axb interaction?
Answers
The df values for the f-ratio for the axb interaction in this experiment would be 28.
To determine the df values for the f-ratio for the axb interaction in this experiment, we first need to calculate the total number of observations in the study. With 3 levels of factor a and 3 levels of factor b, there are a total of 9 possible treatment conditions. With a sample of n = 8 in each treatment condition, there are a total of 72 observations in the study.
Next, we need to calculate the degrees of freedom for the axb interaction. This can be done using the formula dfaxb = (a-1)(b-1)(n-1), where a is the number of levels of factor a, b is the number of levels of factor b, and n is the sample size.
In this case, a = 3, b = 3, and n = 8, so dfaxb = (3-1)(3-1)(8-1) = 2 x 2 x 7 = 28.
Therefore, the df values for the f-ratio for the axb interaction in this experiment would be 28. This indicates the amount of variability in the data that can be attributed to the interaction between factor a and factor b, after accounting for any main effects. A larger f-ratio with a corresponding smaller p-value would suggest a more significant interaction effect.
To know more about df values, refer to the link below:
https://brainly.com/question/28236335#
#SPJ11
Need help with this question
Answers
Answer:
D
since 45027/3 is is 15009 and 804597/3 is 268199
Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
One week a student exercised 3 hours at school and another of an hour at
home. If of the student's total exercise came from playing basketball, how
much time did the student spend playing basketball that week? Enter your
answer in hours; do not include units in your answer.
Answers
The number of hours in a week a student played basketball is \(11\frac{3}{8}\).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.
Also given that 1/4 of the exercise of a student came from playing basketball.
Therefore, Time playing basketball is one-fourth of the total time exercised which is,
= (3 + 1/4)×(1/4).
= (13/4)×(1/4).
= (13/8).
Therefore, In a week the student played (13/8)×7.
= 91/8.
= \(11\frac{3}{8}\).
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
Using the distributive property, which of the following is the expanded form of −14(−8x+12y)
?
Answers
Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.
The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.
So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:
(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)
= (1/4) × 8x − (1/3) × 12y
= 2x − 3y
Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.
To learn more about distributive property here:
https://brainly.com/question/29048637
#SPJ1
solve for x and find the value of x
Answers
We can write an equation for the interior angles, and we will see that x = 13
How to find the value of x?We want to find the value of x, we can see two adjacent angles on a rectangle, then the sum of these two is equal to 180°, we can write:
3x + 78 + x + 50 = 180
4x + 128 = 180
4x = 180 - 128
4x = 52
x = 52/4 = 13
The value of x is 13.
Learn more about interior angles at:
https://brainly.com/question/24966296
#SPJ1
find a recurrence relation for the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b.
Answers
To find a recurrence relation for the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b, we can use the following approach.
Let's consider the last two letters of the sequence. There are three possible cases:
1. The last letter is not "a": In this case, we can append any of the three letters (a, b, or c) to the end of an (n-1)-letter sequence that satisfies the given condition. This gives us a total of 3 times the number of (n-1)-letter sequences that satisfy the condition.
2. The last letter is "a" and the second to last letter is "b": In this case, we can append any of the two letters (a or c) to the end of an (n-2)-letter sequence that satisfies the given condition. This gives us a total of 2 times the number of (n-2)-letter sequences that satisfy the condition.
3. The last letter is "a" and the second to last letter is not "b": In this case, we cannot append any letter to the end of the sequence that satisfies the condition. Therefore, there are no such sequences of length n in this case.
Putting all these cases together, we get the following recurrence relation:
f(n) = 3f(n-1) + 2f(n-2), where f(1) = 3 and f(2) = 9.
Here, f(n) denotes the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b.
Learn More About Recurrence Relation: https://brainly.com/question/4082048
#SPJ11
A researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression: TestScore = 520.4 - 5.82.CS, R2 = 0.08, SER = 11.5 What is the sample standard deviation of test scores across the 100 classrooms? (Hint: Review the formulas for the R2 and SER).
Answers
The sample standard deviation of test scores across the 100 classrooms is 11.9.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation implies that the values are dispersed over a wider range, a low standard deviation shows that the values tend to be close to the mean of the collection.
As given,
Test score = P₀ + (B₁ × cs)
Substitute values respectively,
Test score = 520.4 + (-5.82 × 21.4)
Test score = 395.852
Thus, sample average Test score = 395.852.
Evaluate Sum of Squares Regression (SSR) as follows:
SER = 11.5 then
SSR = (n -2) (SER)²
Substitute values,
SSR = (100 - 2) (11.5) ²
SSR = 12960.5
Evaluate Total Sum of Squares (SST) as follows:
SST = SSR / (1 - R²)
SST = 12960.5 / (1-0.08)
SST = 14087.5
Evaluate standard deviation as follows:
Standard deviation = √ (SST/(n - 1))
Substitute values,
Standard deviation = √ (14087.5 / (100 - 1))
Standard deviation = √ (14087.5/99)
Standard deviation = 11.93
Standard deviation = 11.9
Hence, The sample standard deviation of test scores across the 100 classrooms is 11.9.
To learn more about Standard deviation from the given link.
https://brainly.com/question/24298037
#SPJ4
The long hand of the clock is about 5 inches long. How far does the end of the long hand of the clock travel in 2 1/2 hours?
Answers
The end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.
What is clock ?
Clock can be defined as a machine in which a device that performs regular movements in equal intervals of time is linked to a counting mechanism that records the number of movements
The long hand of the clock completes one full revolution in 12 hours. Therefore, in one hour, it travels a distance equal to the circumference of a circle with a radius of 5 inches, which is given by 2πr = 2π(5) = 10π inches.
In 2 1/2 hours, the long hand of the clock travels a distance equal to (2 1/2) x 10π = 25π inches.
So, the end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.
Learn more about clock here : brainly.com/question/82007
#SPJ1
find all values of x such that (6, x, −11) and (5, x, x) are orthogonal. (enter your answers as a comma-separated list.)x = ___
Answers
The values x such that (6, x, −11) and (5, x, x) are orthogonal is 6,5.
The orthogonal vectors have dot product to be zero. Thus, the formula to be used is -
a . b = a1b1 + a2b2 + a3b3, where a1, a2 and a3 are components a vector and b1, b2 and be are components of b vector.
Keep the values in formula -
a . b = 6(5) + x² + (-11)x
a . b = 30 + x² - 11x = 0
So, x² - 11x + 30 = 0
x(x - 6) - 5(x - 6) = 0
(x - 6) (x - 5) = 0
So, the value of x is 6,5.
Learn more about orthogonal vector -
https://brainly.com/question/15587050
#SPJ4
A random sample of size n= 225 is to be taken from an exponential population with θ=4. Based on the central limit theorem, what is the probability that the mean of the sample will exceed 4.5?
Answers
The central limit theorem, the probability that the mean of a random sample, taken from an exponential population with θ=4, will exceed 4.5 can be determined. The probability associated with the z-score of 1.875.
The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. In this case, since the population distribution is exponential with θ=4, the mean and variance of the population are both equal to 4.
To find the probability that the sample mean exceeds 4.5, we need to standardize the distribution of the sample means using the formula for the standard error of the mean: standard deviation divided by the square root of the sample size. For the exponential distribution, the standard deviation is equal to the mean, which is 4 in this case. Therefore, the standard error of the mean is 4 / sqrt(225) = 4 / 15.
Next, we calculate the z-score, which measures the number of standard deviations the sample mean is away from the population mean. The z-score is calculated as (4.5 - 4) / (4 / 15) = 1.875.
Using a standard normal distribution table or a statistical software, we can find the probability associated with the z-score of 1.875. This probability represents the likelihood that the mean of the sample will exceed 4.5.
Learn more about distribution here:
https://brainly.com/question/29664127
#SPJ11
pls help
In Miss McGee's homeroom, there are 5 blonds, 9 brunettes, 2 redheads, and 2 students with black hair. If Miss McGee chose a student at random, what is the probability that the student would be a red head
Answers
Answer:
2/18 or if needed simplified 1/9. count all the people you get 18 the red head is 2.
Answer:
2 out of 18
Step-by-step explanation:
5+2+2+9= 18 redheads = 2
You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The arch over the road is in the shape of a half-ellipse that is 40 feet wide at the base of the arch and it is 15 feet tall at the center of the arch. The bridge must have a 13-foot clearance for vehicles on the road. The 22-foot-wide road is centered directly beneath the highest point of the arch. a) the semi-truck will NOT be able to pass under the bridge,so it is time to make an adjustment. You will need to modify the design of the bridge. Keep the arch shape as half an ellipse, and the base as 40 feet wide. You may adjust the bridge’s arch up to 18 feet above the center line of the two-lane road below, but no more than that because of restrictions concerning the road crossing over the bridge. Give a new equation for the ellipse that represents your modified design.
Answers
We are asked to determine the equation of an ellipse that has a base of 40 feet and a height of 18 feet. This can be visualized in the following diagram:
The general form of the equation of an ellipse is:
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)We have set the origin of the coordinate system to be in the middle of the ellipse. The value of "a" is the x-intercept of the ellipse and the value of "b" is the y-intercept of the ellipse. Therefore, the equation is:
\(\frac{x^2}{(20)^2}+\frac{y^2}{(9)^2}=1\)Now, we solve the squares:
\(\frac{x^2}{400}+\frac{y^2}{81}=1\)And thus we have determined the equation of the ellipse.
The area of a kite is 51. 68 square inches. One diagonal measures 15. 2 inches. What is the measure of the other diagonal? 3. 4 inches 6. 8 inches 13. 6 inches 15. 2 inches.
Answers
The measure of the other diagonal line is 6.8 inches
A kite is a quadrilateral with two distinguishable consecutive sides. The area of a kite can be calculated by the multiplication of the two diagonal lines divided by 2.
Mathematically, we have:
\(\mathbf{A = \dfrac{pq}{2}}\)
where:
A = area of the kite = 51.68 inches²Let the first diagonal length be p = 15.2 inchesThe other diagonal length q = ???∴
Using the formula for an area of a kite to determine the other diagonal length, we have:
\(\mathbf{51.68 \ inches^2 = \dfrac{15.2 \ inches \times q}{2}}\)
\(\mathbf{q = \dfrac{51.86 \ inches^2 \times 2}{15.2 inches} }\)
q = 6.8 inches
Learn more about the area of kite here:
https://brainly.com/question/2292872
Combine like terms y+6-2-4y3-5y+2y3-2y3
Answers
Answer: -3y+12
Step-by-step explanation:
Camillo needs 2,400 oz of peanut butter. what size container should camillo but?
Answers
Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.
To calculate the size of the container Camillo should buy, we need to find a container size that can accommodate the required 2,400 oz of peanut butter.
By comparing the given container sizes, we can see that the 40-oz container is the largest one available. As Camillo needs 2,400 oz of peanut butter, he would need to purchase multiple containers.
To find out how many of those containers Camillo will need, we can divide the total amount of peanut butter needed (2,400 oz) by the size of each container (40 oz). This gives us:
Number of containers = Total amount needed / Size of each container
Number of containers = 2,400 oz / 40 oz
Number of containers = 60 containers
So Camillo would need to buy 60 of the 40-oz containers to meet his requirement.
To calculate the total cost of those containers, we need to multiply the number of containers (60) by the price of each container. The price for each 40-oz container is $12.40. Therefore:
Total cost = Number of containers * Price per container
Total cost = 60 containers * $12.40
Total cost = $744.00
Hence, the total cost of the 60 containers would be $744.00.
In summary, Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.
To know more about Ratios and Proportions here
https://brainly.com/question/29774220
#SPJ4
Complete Question
Camillo needs 2,400 oz of peanut butter.
What size container should Camillo buy?
How many of those containers will he need?
What will be the total cost of those containers?
Container Size Price Unit Price
12-oz $2.52 $0.21/oz
16-oz $4.00 $0.25/oz
32-oz $5.12 $0.16/oz
40-oz $12.40 $0.31/oz
Need help on this question as well
Answers
The required arc length of sector VW is 8\(\pi\).
Given that, in a circle U, radius UV = 9 and central angle of sector m∠VUW = 160°.
To find the arc length of sector VW, we can use the formula:
Arc length = (central angle / 360) x circumference of the circle.
First, find the circumference of the circle by the formula for the circumference of a circle is given by:
Circumference = 2 x \(\pi\) x radius.
Circumference = 2 x \(\pi\) x 9 = 18π.
Now, let's find the arc length of sector VW using the central angle of 160 degrees:
Arc length = (160/360) x 18π
Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).
Therefore, the arc length of sector VW is 8\(\pi\).
Learn more about arc length of sector click here:
https://brainly.com/question/28988267
#SPJ1
WILL GIVE BRAINLIEST!!
A line has a slope of 1/3 and passes through the point (–9, –3). What is its equation in slope-intercept form?
Answers
Answer:
y = \(\frac{1}{3}\) x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = \(\frac{1}{3}\) , then
y = \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation
- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )
0 = c
y = \(\frac{1}{3}\) x + 0 , that is
y = \(\frac{1}{3}\) x
2. C is at (-5.1) & D is at (7.6). Where is the midpoint on segment CD?
Answers
Answer:
1.25
Step-by-step explanation:
Find the average.
-5.1+7.6=2.5
2.5/2
1.25
if f (x) = 3, what is the value of f (-7)
A. x -10
B. 3
C. -4
D. -21
Answers
Answer:
D
Step-by-step explanation:
3*(-7)=(-21)
A constant function is a function that has the same output with different inputs.
The value of f(-7) for the function f(x) = 3 is 3.
What is a constant function?A constant function is a function that has the same output with different inputs.
It is a function having the same value of range for different values of the domain.
Example: f(x) = 9
f(1) = 0
f(2) = 6
Domain = inputs = 1, 2
Range = outputs = 9
We have,
f(x) = 3
This is a constant function.
So any value of x will always give the output as 3.
f(-7) = 3.
Thus the value of f(-7) for the function f(x) = 3 is 3.
Learn more about constant functions here:
brainly.com/question/19595873
#SPJ2
(11-8)to the 3rd power-2x6
Answers
Answer:
15
Step-by-step explanation:
If the dimensions of a prism with surface area 42 m^2 and volume 18 m^3 are enlarged by a factor of 4, what is the surface area and volume of the prism?
Answers
Surface area = 2xy + 2xz + 2yz = 42
Volume = xyz = 18
We can use these equations to solve for the individual dimensions. First, we can solve for z in terms of x and y from the surface area equation:
2xy + 2xz + 2yz = 42
2z(x + y) = 42 - 2xy
z(x + y) = 21 - xy
Next, we can substitute this expression for z into the volume equation and solve for x and y:
xyz = 18
xy(21 - xy) = 18
21xy - xy^2 = 18
xy^2 - 21xy + 18 = 0
(xy - 2)(xy - 9) = 0
So, either xy = 2 or xy = 9. Since the dimensions of a prism must be positive, we can only use the solution xy = 9. Solving for x and y gives:
xy = 9
x + y + z = 21/xy = 7/3
x = 3, y = 3, z = 1/3
Now, we can scale up the dimensions by a factor of 4 to get the new dimensions of the enlarged prism:
x' = 4x = 12
y' = 4y = 12
z' = 4z = 4/3
The surface area and volume of the enlarged prism are then given by:
Surface area = 2x'y' + 2x'z' + 2y'z' = 576
Volume = x'y'z' = 64
Therefore, the surface area of the enlarged prism is 576 m^2 and the volume is 64 m^3.
SA = 2lw + 2lh + 2wh = 42 m^2 ... (1)
And the volume of the original prism is given by:
V = lwh = 18 m^3 ... (2)
If you enlarge the dimensions of the prism by a factor of 4, then the new dimensions will be 4l, 4w, and 4h. The new surface area of the prism will be:
New SA = 2(4l)(4w) + 2(4l)(4h) + 2(4w)(4h)
= 32lw + 32lh + 32wh
= 32(2lw + 2lh + 2wh)
= 32(42)
= 1344 m^2
So, the surface area of the enlarged prism is 1344 m^2.
Similarly, the new volume of the prism will be:
New V = (4l)(4w)(4h)
= 64lwh
= 64(18)
= 1152 m^3
So, the volume of the enlarged prism is 1152 m^3.
Therefore, the surface area of the prism is 1344 m^2 and the volume of the prism is 1152 m^3 after the dimensions are enlarged by a factor of 4.
*IG:whis.sama_ent
In Exercises 11–14, find the value(s) of h for which the vectors are linearly dependent. Justify each answer. - 3 6 2 -2 4 -6 11. -2 2 h . 4 [:] [:] [1] - [:11:11 LIEL [:] [3] [1] [2] [3] [!] El 1 5 3 h 13. 14. 6 6
Answers
For Exercises 11 and 13, there are no values of h that make the vectors linearly Dependent. For Exercise 14, additional information is required to determine the linear dependence.
To determine the value(s) of h for which the vectors are linearly dependent, we need to check if there exists a scalar k such that one vector is a scalar multiple of the other.
11. The given vectors are [-3, 6, 2] and [-2, 2, h]. To check for linear dependence, we set up the equation:
[-3, 6, 2] = k * [-2, 2, h]
By comparing corresponding entries, we get the following equations:
-3 = -2k
6 = 2k
2 = hk
From the first equation, we can solve for k:
k = 3/2
Substituting this value of k into the second equation, we find:
6 = 2 * (3/2)
6 = 3
This equation is not true, indicating that there is no value of h that makes the vectors linearly dependent. Therefore, the vectors are linearly independent for all values of h.
13. The given vectors are [1, 5, 3, h] and [1, 2, 3, 1]. To check for linear dependence, we set up the equation:
[1, 5, 3, h] = k * [1, 2, 3, 1]
By comparing corresponding entries, we get the following equations:
1 = k
5 = 2k
3 = 3k
h = k
From the first equation, we find that k = 1. Substituting this value into the other equations, we find:
5 = 2 * 1
5 = 2
This equation is not true, indicating that there is no value of h that makes the vectors linearly dependent. Therefore, the vectors are linearly independent for all values of h.
14. The given vectors are [6, 6] and [:]. Since the second vector is missing, it is not possible to determine if the vectors are linearly dependent or independent. More information is needed to solve this problem.
In summary, for Exercises 11 and 13, there are no values of h that make the vectors linearly dependent. For Exercise 14, additional information is required to determine the linear dependence.
For more questions on Dependent.
https://brainly.com/question/25223322
#SPJ8
What are the next two numbers in this sequence? 0, 1, 3, 6, 10, ___, ___
A. 17, 25
B. 15, 21
C. 16, 23
D. 14, 19
Answers
Answer:
b
Step-by-step explanation:
your answer is b to be precise
Beverly fpund a magic bean. If she puts it in the soil , every single day it will grow 4 cm. After how many days will it be 14.56 meters tall
Answers
Answer:
364 days
Step-by-step explanation:
Magic bean will take 364 days to grow 14.56 m tall.
What is Unit Conversion?A conversion factor exists as a ratio that expresses how many of one unit stand equal to another unit. For example, there exist 12 in. in 1 ft, 1609 m in 1 mi, 100 cm in 1 m, 60 s in 1 min, and so on.
Unit conversion exists as a multi-step procedure that involves multiplication or division by a numerical factor, choosing the accurate number of significant digits, and rounding.
First we need to convert the height in m into cm.
14.56 m=14.56*100=1456 cm
If it grows 4 cm in one day then:
It will take 1456/4=364 days (a year) to grow completely.
To know more about unit conversion refer:
https://brainly.com/question/6243489
#SPJ2
WILL MARK BRAINLEST
California's traffic People love living in California for many reasons , but traffic isn't one of them . Based on a random sample of 572 employed California adults, a 90 % confidence interval for average travel time to work for all employed California adults is 23 minutes to 26 minutes
(A) Interpret the confidence level
(B) Name two things you could do to reduce the margin of error. What drawbacks do these actions have?
(C) Describe how no responses might lead to bias in this survey.Does the stated margin of error account for this possible bias?
Answers
90% of all samples have a confidence interval that contains the right average travel time for all employed adults in California.
What is a confidence interval?Increased Sample Size: This provides more information about the population and allows us to calculate an accurate estimate. Data collection is expensive and time-consuming.
Decrease in Confidence Level: Confidence interval having correct population interval is less confident. It has fewer possible values for true population parameters. Hence, it is less confident about the confidence interval has the correct population parameters.
Non-Response Bias
Nonresponse bias happens when there isn't enough data for everyone in the sample. People whose data is unavailable lead to bias and over- or underestimate the true population. The margin of error is not used because it merely takes potential variation into consideration.
To know more about confidence intervals follow
https://brainly.com/question/1290441
#SPJ6