The angle ZB can be computed using the dot product of vectors ZB and ZC, and the area of the triangle can be found using the cross product of vectors ZB and ZC.
To find the angle ZB, we first calculate the vectors ZB and ZC:
[tex]\(ZB = B - Z = (-1, 4, 1) - (4, 10, 7) = (-5, -6, -6)\)[/tex]
[tex]\(ZC = C - Z = (3, 7, 2) - (4, 10, 7) = (-1, -3, -5)\)[/tex]
Then, we calculate the dot product of ZB and ZC:
[tex]\(ZB \cdot ZC = (-5, -6, -6) \cdot (-1, -3, -5) = 43\)[/tex]
Using the dot product formula, we can find the angle between the two vectors:
[tex]\(\cos(ZB) = \frac{{ZB \cdot ZC}}{{\|ZB\| \cdot \|ZC\|}} = \frac{{43}}{{\sqrt{77} \cdot \sqrt{35}}}\)[/tex]
Finally, we can calculate the angle ZB using the inverse cosine function:
[tex]\(ZB = \cos^{-1}\left(\frac{{43}}{{\sqrt{77} \cdot \sqrt{35}}}\right)\)[/tex]
To find the area of the triangle formed by the three points, we calculate the cross product of vectors ZB and ZC:
[tex]\(ZB \times ZC = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -5 & -6 & -6 \\ -1 & -3 & -5 \end{vmatrix}\)[/tex]
By expanding the determinant, we obtain the resulting vector:
[tex]\(ZB \times ZC = (12, -1, -9)\)[/tex]
The magnitude of this vector represents the area of the triangle:
[tex]\(\text{Area} = \left\|ZB \times ZC\right\|\)[/tex]
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Round 61219.4439681 to the nearest thousand
Answer:
6100
Step-by-step explanation:
I think its 1600
Answer: 61219.444
Step-by-step explanation:
The decimal will go 3 times to the right on the nearest thousandths place.
~I hope I helped you! :)~
IXL learning diagnostic
What is 200000-56330
Answer:
143670
Step-by-step explanation:
200000
- 56330
_________
143670
Data Set 20
$3.04 $7.07 $2.82 $3.03 $3.28 $4.91 $4.09 $5.49 $5.02 $4.15 $4.53 $3.06 $5.56 $6.08 $2.87 $4.56 $5.20 $2.48 $4.12 $3.55 $3.49 $6.24 $5.01 $2.43 $4.70 $2.31 $7.41 $7.09 $4.81 $6.62 From the data set of fuel prices above; · Find the mean and standard deviation for the data set. Please do not try to do this by hand, but use the functions in Excel. · Find the Confidence Interval for your data. Sample initial post: First find the mean and standard deviation.
Then put this in an excel cell =confidence.norm(0.5,stdev,samplesize) and hit enter. This is the E value. (Note: please use your standard deviation and sample size and not the words.)
Set up your confidence interval: (mean-E, mean+E)
Formula you used above for the confidence interval:
The formula is E= zsubc * sigma / sqrt n
Where the left hand endpoint is xbar - E and the right hand endpoint is xbar + E
The mean of the given fuel prices data set is $4.61 with a standard deviation of $1.62.
To calculate the mean and standard deviation in Excel, you can use the following functions:
Mean: The AVERAGE function calculates the mean of a range of values. In this case, enter "=AVERAGE(A1:A30)" in an Excel cell, assuming the data is in cells A1 to A30.
Standard Deviation: The STDEV.S function calculates the standard deviation of a range of values. Enter "=STDEV.S(A1:A30)" in an Excel cell to calculate the standard deviation of the data set.
Using the mean ($4.61) and standard deviation ($1.62), we can now proceed to calculate the Confidence Interval.
The Confidence Interval can be determined using the formula: E = Z * (σ / √n)
In the formula, Z is the z-score corresponding to the desired level of confidence (e.g., 95% confidence corresponds to a z-score of approximately 1.96), σ is the population standard deviation (which can be estimated using the sample standard deviation in this case), and n is the sample size.
Let's assume we want a 95% confidence interval for the data set with a sample size of 30. We can use the formula "=CONFIDENCE.NORM(0.05, STDEV, 30)" in an Excel cell to calculate the E value.
Substituting the values into the formula, we get E = 1.96 * (1.62 / √30) ≈ 0.595.
Now, we can set up the confidence interval using the mean and E value:
Confidence Interval = (mean - E, mean + E)
Confidence Interval = ($4.61 - $0.595, $4.61 + $0.595)
Confidence Interval = ($4.015, $5.205)
Therefore, the 95% Confidence Interval for the given fuel prices data set is approximately $4.015 to $5.205.
In summary, the mean of the fuel prices data set is $4.61 with a standard deviation of $1.62. The 95% Confidence Interval for the data is approximately $4.015 to $5.205.
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escribe how relative frequencies of past events are used to predict future events. (for example, if a student passed seven out of ten assignments in a course, what do you think is the probability that this student will pass the next assignment in the course? how did you calculate this probability?)
Relative frequencies of past events can be used to predict future events by using probability theory. Probability theory is a branch of mathematics that deals with the study of random phenomena.
In the given example, if a student passed seven out of ten assignments in a course, the probability that the student will pass the next assignment in the course can be calculated by using relative frequency. We can use the formula of probability to calculate the probability of the student passing the next assignment. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the number of favorable outcomes is seven because the student passed seven out of ten assignments. The total number of possible outcomes is ten because the student attempted ten assignments. Therefore, the probability of the student passing the next assignment is 7/10 or 0.7. This means that there is a 70% chance that the student will pass the next assignment.
In conclusion, the relative frequency of past events can be used to predict future events. Probability theory can be used to calculate the probability of an event occurring in future events. By using the formula of probability, we can calculate the probability of an event occurring based on the relative frequency of past events. In the given example, the probability of the student passing the next assignment is calculated as 0.7 or 70%.
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The school café charges $3 for hot lunch. This amount is automatically withdrawn from a student's lunch account each day they purchase. If Kelsey purchased hot lunch all 5 days last week, how much did her lunch account change?
Answer:
15 dollars
Step-by-step explanation:
you do 3 × 5 which will give you 15
A cone-shaped paper drinking cup is to be made to hold 36 cm^3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
height 4.10 cm
radius ____ cm
A cone-shaped paper drinking cup is to be made to hold 36 cm^3 of water. In order to make the paper cup with the least amount of paper, we need to minimize the surface area of the cone.
We want to minimize the surface area of the cone, which is given by:S = πr(r + s)where s is the slant height of the cone. We can eliminate s by using the Pythagorean theorem: s^2 = r^2 + h^2hence: s = sqrt(r^2 + h^2)
Now, we can substitute this into the surface area formula: S = πr(r + sqrt(r^2 + h^2)) = πr^2 + πr(sqrt(r^2 + h^2))
To minimize the surface area, we need to find the values of r and h that satisfy the volume equation and minimize the surface area equation. We can do this by using the method of Lagrange multipliers. The Lagrangian function is: L = πr^2 + πr(sqrt(r^2 + h^2)) + λ[(1/3)πr^2h - 36] Taking partial derivatives with respect to r, h, and λ and setting them equal to zero gives: 2πr + (πh r)/(sqrt(r^2 + h^2)) + (2/3)πλr^2 = 0πr/(sqrt(r^2 + h^2)) + (1/3)πλr^2 = 0(1/3)πr^2h - 36 = 0 Solving this system of equations gives:r = 1.85 cm h = 4.10 cmλ = 0.57 cm^-1
Therefore, the radius of the paper cup that uses the smallest amount of paper is 1.85 cm. The height of the paper cup that uses the smallest amount of paper is given as 4.10 cm. The radius of the paper cup that uses the smallest amount of paper is found to be 1.85 cm.
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Lines m and n are parallel lines. If line m has a slope of -2, find the slope of line n. Type a numerical answer in the space provided. If necessary, use the / key as a fraction bar. Do not type spaces in your answer.
Answer:
slope=-2
Step-by-step explanation:
If two lines are parallel, they have the same slope with different y-intercept
i need help plssssss:/
Answer:
B and the last one. not a taxi is the best taxi and
Step-by-step explanation: BUHNROP (SPELL IT BACKWORDS THAT IS MY FAVORITE SHOW EVER!!!
The coefficient of x^5y^3 in the expansion of (x+4y)^8 is
Answer:
hahahahaha hacker lang poStep-by-step explanation:
ibig sabihin points lang habol ko sorry guys(i) A person borrowed Rs. 16000 from a bank at 12.5% per annum simple interest for 3 years and but he loans the whole amount to a shopkeeper at the same rate of compound interest for the same time.
(a) Find the amount to be paid to the bank as simple interest.
(b) Find the amount to be get to the shopkeeper as compound interest.
(c) How much will he gain after 3 years?
The person will gain Rs. 5,500 after 3 years by lending the whole amount to a shopkeeper at the same rate of compound Interest for the same time.
Given, Principal amount (P) = Rs. 16,000
Rate of Interest (R) = 12.5%
Time (T) = 3 years(a)
The amount to be paid to the bank as simple interest can be calculated as follows:
Simple Interest (SI) = (P × R × T) / 100= (16000 × 12.5 × 3) / 100= Rs. 6,000Therefore, the amount to be paid to the bank as simple interest is Rs. 6,000.
(b) The amount to be received by the person from the shopkeeper as compound interest can be calculated as follows: Compound Interest (CI) = P × [1 + (R/100)]T – P= 16000 × [1 + (12.5/100)]3 – 16000= Rs. 21,500
Therefore, the amount to be received by the person from the shopkeeper as compound interest is Rs. 21,500.(c) Gain = CI - P= 21500 - 16000= Rs. 5,500
Therefore, the person will gain Rs. 5,500 after 3 years by lending the whole amount to a shopkeeper at the same rate of compound interest for the same time.
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What is 1.71×10 7th power written in standard form?
Answer:
17100000
17100000
Step-by-step explanation:
Answer:
17,100,000
Step-by-step explanation:
Hope this helped:)
3. How many solutions does the system of equations have?
a,b and c are points on a circle such that bc bisects angle abq,pbq is a tangent to the circle and angle cbq =x
Answer:
Step-by-step explanation:
Write an equation for each line.Equation of the line in the slope - intercept form is...?
Answer:
y=(-5/9)x+0.25
Ms. Armstrong purchased a car for $20,000. After 4 years, the car was only worth $8,000. Write an equation in slope intercept form that can be used to find the value of the car y, after x number of years.
Answer:
$20,000=4x
Step-by-step explanation:
First if we want to find out how much the price of the car went down we would have to find out how much the price went down by subtracting $20,000 by $8,000. I got 12,000. Then we have to find out how much the price went down every year. So, $12,000 ÷ 4 = $3,000. So, in 4 years the price went down $3,000 dollars every year
Find the rule for the following set of data.
y =
2/5 x + 31/5
5/2 x - 2
5/2 x + 2
Answer:
[tex]y = \frac{5}{2} x + 2[/tex]
Step-by-step explanation:
Find slope which is also referred to as m:
m = (y2 - y1) / (x2 - x1)
= 7-12 / 2 - 4
= -5 / -2
= 5/2
y = mx + b
17 = 5/2(6) + b
17 = 15 + b
b = 2
y = 5/2x + 2
Does this graph represent a function? Why or why not?
What is true about the number 2.89? Check all that apply.
2.89 should be plotted between 2.8 and 2.9.
2.89 is closer to 2.0 than 3.0.
2.89 is closer to 3.0 than 2.0.
2.89 is closer to 2.8 than 2.9.
2.89 is closer to 2.9 than 2.8.
Which expression is equivalent to t + 4 + 3 -2
Answer:
t + 5 ; 5 + t; t + 7 - 2;
Step-by-step explanation:
there are many more but these are some examples
Subtract 0.64 -0.38.
0.26
1.00
1.02
1.26
Answer:
The answer to 0.64 - 0.38 is 0.26
Step-by-step explanation:
hope this helps!!!
help me if u can please
A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.
How much will a group of 12 students save by choosing the science center?
Answer:
use math papa
Step-by-step explanation:
Answer:
they will save 6$ hope this helps !!
I need help with this question
Answer:
Value of x is 23.
Step-by-step explanation:
7x-5+x+1=180
after solve
we get
x = 23
⚠️IN NEED THIS IN THE NEXT 30 MIN ⚠️
Suppose you already have $20, and you friend already has $10. You make $15 per hour, and you friends makes $15 per hour, at a job. In how many hours will it take you and your friend to have the total amount of money? This is a system which has....
A. Not enough info to determine the solution
B. Infinitely many solutions
C. 0 solutions
D. 1 solution
Answer:
b because it never said how much many you and your friend need
Step-by-step explanation:
22 The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83? a. 98 b. 39 c. 6
d. 148 e.49
The approximate number of students with Scores between 68 and 83 is 98.Answer: a. 98
The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83?
The five-number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.
The interquartile range is the difference between the third and first quartiles. Interquartile range (IQR) = Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. The 5-number summary for scores on a statistics exam is given below:
Minimum value = 35
First quartile Q1 = 68
Median = 77
Third quartile Q3 = 83
Maximum value = 97
The interval 68–83 is the range between Q1 and Q3.
Thus, it is the interquartile range.
The interquartile range is calculated as follows:IQR = Q3 – Q1 = 83 – 68 = 15
The interquartile range of the scores between 68 and 83 is 15. Therefore, the number of students with scores between 68 and 83 is roughly half of the total number of students. 196/2 = 98.
Thus, the approximate number of students with scores between 68 and 83 is 98.Answer: a. 98
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Please help lol rrly fast thxxxxxx
Make a stem-and-leaf plot to display the data set.
41, 41, 44, 55, 58, 59, 60, 61, 62, 63, 72, 77
The stem-and-leaf plot for the data-set in this problem is given as follows:
4|1 1 4
5|5 8 9
6|0 1 2 3
7|2 7
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
The stems for this problem are the first digits of the numbers, which are 4, 5, 6 and 7.
The leafs are the second digits, hence the plot is given as follows:
4|1 1 4
5|5 8 9
6|0 1 2 3
7|2 7
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I please help with this question
A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. If specifications call for the ladder's angle of elevation to be between 35 and 45 degrees.
Given the information above, sketch out the scenario. Determine if the placement of this ladder satisfies safety specifications. Then, explain why or why not it would meet the safety specifications using at least 3 complete sentences.
Answer:
Step-by-step explanation:
Note that the base of the building forms a right angle with the ground and the ladder forms a right triangle with the building.
On this case, we can apply Pythagorean theorem.
Since the ladder serves as the hypotenuse and the distance from the base of the building to the foot of the ladder is adjacent with the angle of elevation, we can use cosine.
Let A be the angle of elevation
cos A = adjacent/hypotenuse
cos A = 10ft/20ft
cos A = 0.50
A = Arc cos 0.50
A = 60°
With the given data, the angle of elevation turns out to be 60°. As it's beyond the allowable values, it won't satisfy the safety specifications of 35°-45°. The placement of the ladder is too steep and would need to be adjusted.
