Coordinates of the midpoint [tex](h,k)[/tex] of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]h=\frac{x_1+x_2}{2}[/tex]
[tex]k=\frac{y_1+y_2}{2}[/tex]
If the coordinates of the endpoints D, F and midpoint E are [tex](x_1,y_1)[/tex], [tex](5,8)[/tex] and [tex](4,3)[/tex] respectively,
Coordinates of the endpoint D,
[tex]4=\frac{x_1+5}{2}[/tex]
[tex]x_1+5=8[/tex]
[tex]x_1=3[/tex]
[tex]3=\frac{8+y_1}{2}[/tex]
[tex]y_1+8=6[/tex]
[tex]y_1=-2[/tex]
Therefore, coordinates of the endpoint D are [tex](3,-2)[/tex].
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We have that the coordinates of the missing endpoint is
d=(13,14)
From the question we are told that
The coordinates of the missing endpointE is the midpoint of df. f=(5,8) E=(4,3)Generally the equation for the df is mathematically given as
For X
[tex]\frac{(x_1-x-2)}{2}= x_m\\\\\frac{(x_1-5)}{2}= 4[/tex]
x_1-5=8
x_1=13
For Y
[tex]\frac{(y_1-y-2)}{2}= y_m\\\\\frac{(y_1-8)}{2}= 3[/tex]
y_1-8=6
y_1=14
Therefore the coordinates of the missing endpoint
d=(13,14)
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Eleanor can drive an average of 374 miles on one tank of gas. How many miles can she drive on 15 tanks of gas?
Explain how we use a tree diagram to determine the probability of an events
Tree diagrams are a helpful tool for calcuating probabilities when there are several independent events involved. They get their name because these types of diagrams resemble the shape of a tree. The branches of a tree split off from one another, which then in turn have smaller branches. Just like a tree, tree diagrams branch out and can become quite intricate.
The local zoo contracts with one of the local veterinary clinics for pet checkups and sick visites. the zoo manager thought the vet made more then 375 visits to the zoo in one year, but the actual number was 412. what was the percent error between the actual number of visits and the number of visits the manager thought the vet made
From a group of 8 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group?
The probability of randomly selecting the 2 oldest people from the group of 8 is approximately 0.0357 or 3.57%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The total number of possible ways to select 2 people from a group of 8 is given by the combination formula:
C(8,2) = 8! / (2! x 6!) = 28
This means that there are 28 different pairs of people that can be selected from the group of 8.
To calculate the probability that the 2 oldest people are selected, we need to first determine how many ways there are to select these 2 people.
Since the order in which we select the people does not matter, we can simply choose any 2 people from the group of 8 in order to select the 2 oldest people.
There are C(8,2) = 28 ways to select any 2 people, and since there is only 1 pair that consists of the 2 oldest people, the number of ways to select the 2 oldest people is 1.
Now,
The probability of selecting the 2 oldest people is:
1/28 = 0.0357
Thus,
The probability of randomly selecting the 2 oldest people from the group of 8 is approximately 0.0357 or 3.57%.
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Final answer:
To find the probability of selecting the two oldest people from a group of 8, we calculate the number of ways to choose 2 people from 8 (28 ways) and understand that there is only 1 way to choose the two oldest. Thus, the probability is 1/28.
Explanation:
The question asks about the probability of selecting the two oldest people from a group of 8. To solve this, we can use the concept of combinations. There is only one way to pick the two oldest people. However, the total number of ways to pick 2 people out of 8 is calculated using combinations, which can be represented as 8 choose 2 or 8C2. The formula for combinations is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.
Applying this formula, the total number of ways to choose 2 people from 8 is :
8C2 = 8! / (2!(8-2)!) = 28
Therefore, the probability that the two people selected are the oldest is :
Probability = 1 / 28
Nora and Eli are making homemade spring rolls for a party. Nora can make 8 spring rolls in 10 minutes. Eli can make 10 spring rolls in 12 minutes. If they each make 40 spring rolls, who will finish first? ******************************************************Can someone answer this for me please, it's 12 am and I have more work to do, help is very much appreciated**********************************************************
The person who will make 40 spring rolls the fastest is required.
Eli will finish first.
Nora
[tex]10\ \text{minutes}=8\ \text{spring rolls}[/tex]
[tex]1\ \text{spring roll}=\dfrac{10}{8}\ \text{minutes}[/tex]
[tex]40\ \text{spring rolls}=40\times \dfrac{10}{8}=50\ \text{minutes}[/tex]
Eli
[tex]12\ \text{minutes}=10\ \text{spring rolls}[/tex]
[tex]1\ \text{spring rolls}=\dfrac{12}{10}\ \text{minutes}[/tex]
[tex]40\ \text{spring rolls}=40\times \dfrac{12}{10}=48\ \text{minutes}[/tex]
Eli will finish first.
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why can you use addition to check a subtraction
If the parent function is f(x) =x^2 and its transformed fuction is g(x)=2(x-1)^2
What is the value of 11−3m , when m = 2?
5
6
10
12
An airplane flies 2700 miles from Los Angeles to New York City. When the plane flies back to Los Angeles, is it flying in a negative direction? Use absolute value to justify your answer.
the number below follow a pattern
300 30 3 0.3
part a answer is 0.03 0.003
part b
what is the relationship between the terms in the pattern?
Answer:
Part a) the next two numbers of the sequence is 0.03, 0.003
part b)
We get each successive terms, we get previous term divided by 10.
2nd term = 1st term ÷ 10
3rd term = 2nd term ÷ 10
4th term = 3rd term ÷ 10
Step-by-step explanation:
The given number are 300, 30, 3, 0.3
You can see that the previous number divided by 10 to get the next number.
So the next two numbers are
0.3 ÷ 10 = 0.03
0.03 ÷10 = 0.003
Part a) the next two numbers of the sequence is 0.03, 0.003
Part b.
We get each successive terms, we get previous term divided by 10.
2nd term = 1st term ÷ 10
3rd term = 2nd term ÷ 10
4th term = 3rd term ÷ 10
Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground. Find the ground distance from Charlie to the plane. Show how you know
A student found the slope of a line that passes through the points (-8, -6) and (2, -3) to be 3/10.
What mistake did she make?
A - She calculated the run over the rise.
B - She forgot the negative sign.
C - She used the negative reciprocal of the slope.
D - She did not make a mistake. That is the correct slope.
Answer:
Its C, edge 2021
Step-by-step explanation:
No, she did not substitute the correct x and y values.
jude is incorrectly simplified the expression [1/2]^2 times 1/2 times [1/2]^3, as shown below.
[1/2]^2 x 1/2 x [1/2]^3= [1/8]^6 =1/262,144
describe the mistake that jude made. In your explanation , provide the correct way to simplify the expression
Jude incorrectly squared the common base (1/2) when she should have added the exponents. The correct simplification of (1/2) ² × 1/2 × (1/2) ³ is (1/2) ⁵, which equals 1/32.
Jude made a common mistake while simplifying the expression (1/2) ² × 1/2 × (1/2) ³.
Instead of combining the exponents correctly, Jude incorrectly assumed that raising the power of a power would simply entail squaring (1/8), thus ending up with (1/8) ⁶ which equates to 1/262,144.
However, the correct method to simplify the expression involves adding the exponents when multiplying the same base number.
The correct simplification would be (1/2) ⁵ because we have (1/2) ² (twice), then multiplied by 1/2 (once), and then by (1/2) ³ (thrice), so the sum of the exponents is 2+1+3=6.
Therefore, (1/2)⁵ equals 1/32.
Following the rules for powers and exponents ensures that we arrive at the correct mathematical solution.
Simplify 8(x - 4).
8x - 4
x - 32
8x - 32
x - 4
Jesse wants to save the same amount of money each week for a trip. He needs $3,060. If the trip is 36 weeks away how much money should Jesse save each week?
There are 44 books per shelf and there are 8 shelves 1/4 of these books are novels.How many novels will there be??
There will be 88 novels among the total of 352 books.
To find the number of novels, we can use the information that 1/4 of the books are novels.
First, we calculate the total number of books:
Total number of books = 44 books/shelf * 8 shelves
= 352 books
Then, we can find the number of novels:
Number of novels = 1/4 * 352 books
= 88 books
Therefore, there will be 88 novels.
Refer to the spinner. Find the odds of the spinner landing on a dark section.
math question down below
There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes a random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
You must show your working.
A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?
24 students in a class took an algebra test. If 18 students passed the test, what percent do not pass? Question 7 options: A) 6% B) 75% C) 18% D) 25%
The percentage of students that do not pass will be 25%. Then the correct option is D.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
24 students in a class took an algebra test. If 18 students passed the test.
Then the percentage of the students that do not pass will be given as,
P = [(24 - 18) / 24] x 100
P = (6 / 24) x 100
P = 0.25 x 100
P = 25%
The percentage of students that do not pass will be 25%. Then the correct option is D.
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The crab nebula is a cloud of gas and dust particles in space that is expanding at a rate of 930 miles per second. What is its rate of expansion in miles per hour?
x+46=4/5(360) need help solving
Sheryl has a basket of ripe apples and peaches. The number of apples in the basket is 12 more than twice the number of peaches. If there are 36 apples in the basket, there are __ peaches in the basket
What is the perimeter of a triangle with sides of lengths 5, 8, & x?
13 + x
40 + x
40x
21
The high temperature in Fairbanks, Alaska was 15.7 °F one day. That night, the temperature fell 38.4 degrees. What was the low temperature for the night?
Enter your answer as a decimal
Answer:
The low temperature for the night was of -22.7 °F.
Step-by-step explanation:
As the high temperature during the day was 15.7 degrees, but it fell 38.4 degrees in the night, in order to know which was that temperature we have to do the following calculation:
15.7 - 38.4: X (Temperature for the night)
-22.7: X
The low temperature for the night was of -22.7 °F.
Answer:
-22,7 i took the test
Step-by-step explanation:
Simon wanted to find the equation of a line that passes through (–6, 5) and is perpendicular to the graph of 3x + 2y = –11. His work is shown below.
1. 3x + 2y = –11 written in slope-intercept form is y = x , so the slope is .
2. The slope of the perpendicular line is .
3. Substitute the point and the new slope into point-slope form to get y – 5 = (x – (–6)).
4. Simplifying, the line is y – 5 = (x + 6)
"3x + 2y = –11 written in slope-intercept form is y = x." Not so.
To find the slope of this line, solve for y:
2y = -3x - 11 => y = (-3/2)x - 11/2. The slope of the given line is -3/2. The
graph of the new (perpendicular) line will then be the negative reciprocal of -3/2, or +2/3.
Now use the point-slope formula for the equation of a straight line to determine the equation of this new (perpendicular) line thru (-6,5):
y-5 = (2/3)(x+6) (answer)
To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. Using the point-slope form, we can substitute the point and the new slope to get the equation of the perpendicular line.
Explanation:1. To write the given equation in slope-intercept form, we need to solve for y. Rearranging the equation, we have 2y = -3x - 11, y = (-3/2)x - 11/2. Therefore, the slope of the given line is -3/2.
2. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 2/3.
3. Using the point-slope form, we substitute the point (-6, 5) and the new slope (2/3) into the equation y - y1 = m(x - x1), where x1 and y1 are the coordinates of the given point. Plugging in the values, we get y - 5 = (2/3)(x + 6).
4. Simplifying the equation, we can distribute 2/3 to x and 6, which gives us y - 5 = (2/3)x + 4. Adding 5 to both sides, the final equation of the line passing through (-6, 5) and perpendicular to 3x + 2y = -11 is y = (2/3)x + 9.
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the circumference of a circular hot tub in a hotel is 56.5 yards.what is the diameter of the hot tub?
A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured trail mixes?
x < 9.02 or x > 9.48 because |x − 0.23| + 9.25 > 0
x < 9.25 or x > 9.48 because |x − 9.25| > 0.23
x < 9.25 or x > 9.48 because |x − 0.23| + 9.25 > 0
x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Answer:
The correct option is D) x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Step-by-step explanation:
Given:- Each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted.
We need to find out the correct range of rejected masses, X for the manufactured trail mixes
9.25 - 0.23 = 9.02 (It can't weigh less then this)
9.25 + 0.23 = 9.48 (It can't weigh more then this)
Since, rejected masses are : x < 9.02 and x > 9.48
Only option A and D has condition x < 9.02 and x > 9.48
In option A) |x − 0.23| + 9.25 > 0
this is wrong condition because it must be |x − 0.25|
For Option D)
Check:
modulus |x − 9.25| > 0.23 express as
- 0.23 > (x − 9.25) > 0.23
Add 9.25 in above ,
- 0.23 + 9.25 > (x − 9.25 + 9.25) > 0.23 +9.25
9.02 > x > 9.48
True
So, the correct option is D)
x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Which ordered pair is the solution to the system of equations? {−3x+4y=−20{,y=x−4 A.(−4, −8) .B.(−2, −6) C.(4, 8) D.(0, −5)
The solution of the given system of equations is (-4, -8).
Therefore, option A is correct.
Given equations are,
[tex]-3x+4y=-20..........(1)\\\\y=x-4 .........(2)[/tex]
Substituting the value of equation 2 in equation 1.
[tex]-3x+4(x-4)=-20\\\\-3x+4x-16=-20\\\\x=-20+16=-4[/tex]
Substituting the value of x in equation 2
We get, [tex]y=-4-4=-8[/tex]
The solution is (-4, -8)
Therefore, option A is correct.
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