Vector AN = a + ¾ c and we have shown that vector NM = ¼(2a – 3c) where M is the midpoint of line AB and N divides the line BC in the ratio 1:3 .
(a) To express vector AN in terms of a and c, we need to find the vector from A to N. Since N divides BC in the ratio 1:3, we can write:
BN = 3NC
Since M is the midpoint of AB, we have:
AM = MB
Adding these two equations, we get:
AM + BN = MB + 3NC
Substituting the vectors, we get:
a + BN = ½ (a + b + 2c) + 3c
Simplifying, we get:
BN = ½ (b – a) + 2c
But b = 2a – c (since M is the midpoint of AB)
So, we can write:
BN = ½ (2a – 2a + c) + 2c = ¾ c
Therefore, vector AN = vector AB + vector BN = (b – a) + ¾ c
Substituting b = 2a – c, we get:
Vector AN = a + ¾ c
(b) To show that vector NM = ¼(2a – 3c), we need to find vector NM and simplify it. Since M is the midpoint of AB, we have:
Vector NM = vector NC – vector MC
We know that N divides BC in the ratio 1:3, so we can write:
Vector NC = 3/4 vector BC = 3/4 (vector AB + vector AC)
Since M is the midpoint of AB, we have:
Vector MC = 1/2 vector AB
Substituting these vectors, we get:
Vector NM = 3/4 (vector AB + vector AC) – 1/2 vector AB
Simplifying, we get:
Vector NM = 1/4 vector AB + 3/4 vector AC
But AB = 2a – c (since M is the midpoint of AB)
Substituting, we get:
Vector NM = 1/4 (2a – c) + 3/4 c
Simplifying, we get:
Vector NM = ½ a – 3/4 c
Multiplying by 2, we get:
Vector NM = 2/2 (½ a) – 3/4 c
Simplifying, we get:
Vector NM = ¼ (2a – 3c)
Therefore, we have shown that vector NM = ¼(2a – 3c).
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how many minute will a car take to travel
The number of days in which Meena would be able to complete the work alone is 24 days.
How to determine the required number of days?In order to determine the number of days in which Meena would be able to complete the work alone, we would have to assign variables to the amount of time taken by Mala, Meena, and Vinay, and then translate the word problem into an algebraic equation as follows;
Let the variable y represent the number of days taken by Mala.Let the variable x represent the number of days taken by Meena.Let the variable z represent the number of days taken by Vinjay.Note: Combined work rate = 1/x + 1/y + 1/z
Based on the information provided, we have the following equations that models the work rate by each person;
1/(x + y) = 10 ⇒ 1/10 = x + y ........equation 1.
1/(y + z) = 12 ⇒ 1/12 = y + z ........equation 2.
1/(x + z) = 15 ⇒ 1/15 = x + z ........equation 3.
x + y + y + z + x + z = 1/10 + 1/12 + 1/15
2(x + y + z) = 15/60
2(x + y + z) = 1/4
x + y + z = 1/8
From equation 2, we have:
x + (y + z) = 1/8
x + 1/12 = 1/8
x = 1/8 - 1/12
x = 1/24
x = 24 days.
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help me with this please hurry
Answer:
x = -11
Step-by-step explanation:
[tex]3x + 4(3 - \frac{1}{2} x) = 1[/tex]
[tex]3x + 12 - 2x = 1[/tex]
[tex]12 + x = 1[/tex]
[tex]x = - 11[/tex]
Two angles are complementary
Angle 3 = 5x -15
Angle 4 = 3x + 10
What is the measure of angle 4?
The measure of angle 4 is 45.6( nearest degree)
What are complementary angles?Two angles are complementary when the sum of the two angles is 90°. For example if x and y are complementary, then x+y = 90°.
Example of complementary angles are 50 and 40 , 30 and 60 , 25 and 65 e.t.c
Since angle 3 and angle 4 are complementary, therefore, 5x -15 + 3x+10 = 90
5x -15 + 3x+10 = 90
collect like terms
5x+3x -15 +10 = 90
8x -5 = 90
8x = 95
x = 95/8
x = 11.875
Therefore the measure of angle 4 is
3( 11.875) + 10
= 35.625 + 10
= 45.6 (nearest degree)
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Marcia deer foot purchased a $120000,5-year term life insurance policy when she was 55. Now she is 60, what is the percent increase in the premium
The percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.
How to find percent increase in the premium?To calculate the percent increase in the premium for Marcia's life insurance policy, we can use the following formula:
[tex]$Percent increase = \frac{ (New premium - Initial premium)}{ Initial premium} \times 100[/tex]
First, we need to find the initial premium, which can be calculated using the formula for the present value of a term life insurance policy:
[tex]Initial premium = \frac{Face amount of the policy}{Present value factor}= \frac{120,000}{4.3295} = $27,730.25[/tex]
Assuming the same face amount and an interest rate of 5%, the new premium can be calculated as follows:
[tex]New premium= \frac{\text{Face amount of the policy}}{\text{Present value factor}} \ &= \frac{120,000}{3.6962} \ &= $32,466.72 \end{aligned}[/tex]
Now we can use the formula above to calculate the percent increase in the premium:
[tex]Percent increase= \frac{(\text{New premium} - \text{Initial premium})}{\text{Initial premium}} * 100 \ &= \frac{(32,466.72 - 27,730.25)}{27,730.25} * 100 \ &= 17.06% \end{aligned}[/tex]
Therefore, the percent increase in the premium for Marcia's life insurance policy is approximately 17.06%.
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an old refrigerator consumes 202 w of power. assuming that the refrigerator operates for 18 hours every day, what is the annual operating cost of the refrigerator if the cost of electricity is $0.09 per kwh? answer to two decimal places without a unit.
The Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.)
Given:Power consumed by the old refrigerator = 202 WAssuming the refrigerator operates for 18 hours every day.Cost of electricity is $0.09 per kWh.Solution:Power consumed by the old refrigerator in an hour = 202 WTime for which the refrigerator operates every day = 18 hours Energy consumed by the refrigerator in a day = Power consumed × Time = 202 W × 18 hours = 3636 Wh Energy consumed by the refrigerator in a year (365 days) = 3636 Wh × 365 days= 1324740 Wh = 1324.74 kWhCost of electricity is $0.09 per Therefore, Annual operating cost of the refrigerator = Energy consumed × Cost of electricity= 1324.74 kWh × $0.09 per kWh = $119.22 (approx.)Hence, the answer is $119.22 (approx.).
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OFFERING 100 POINTS AND BRAINILEST!! show work please
Answer:
sorry for my pen!......
Solve the equation 101 3/5 =k+33 4/5 for k .
Answer: k = 67 4/5
Step-by-step explanation:
101 3/5 =k+33 4/5
first isolate your variable by subtracting 33 4/5 from both sides
101 3/5 - 33 4/5 = k
now subtract
to subtract 4/5 from 3/5, you have to borrow 5/5 or 1 whole from 101 and add it to 3/5. 5/5 + 3/5 = 8/5. 101 - 1 = 100.
so now you have
100 8/5 - 33 4/5 = k
100 - 33 = 67
8/5 - 4/5 = 4/5
your answer is 67 4/5
Check your work.
67 4/5 + 33 4/5 = 100 8/5 simplified to 101 3/5, our starting number.
solution is true so problem solved!
Insurance Plan Summary
Deductible
$5,000.00
Wellness Exams
No-deductible
100% covered
Premium (monthly)
Individual
Individual+Spouse
A. $400.00
C. $0
$45.00
$4:0.00
What is the monthly
payment an employee
with a family plan on
this health plan is
required to pay, even
if they do not visit a
doctor or hospital?
B. $5,000.00
D. $45.00
the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.
what is insurance ?
Insurance is a contract between an individual or an entity (the insured) and an insurance company (the insurer), in which the insurer agrees to compensate the insured for financial losses or damages that occur due to unexpected events, in exchange for the payment of premiums by the insured.
Based on the information provided, the employee with a family plan is on the "Individual+Spouse" premium plan, which has a monthly premium of $450.00. This means that regardless of whether or not the employee visits a doctor or hospital, they are required to pay this amount every month to maintain their insurance coverage.
Therefore, the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.
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Supreme cookie dough has 25% chocolate chips. Magic cookie dough has 35% chocolate chips. Samantha mixes 4 cups of Supreme cookie dough with 4 cups of Magic cookie dough. Enter the percent of chocolate chips in the mixture.
The percent of chocolate chips in the mixture is a total of 30% as supreme cookie dough has 25% chocolate chips and Magic cookie dough has 35% chocolate chips.
Let one cup be equal to one gram,
therefore, one cup or gram of supreme cookie dough has 25% of chocolate cookie dough
25% of 4 cups = 25/100 x 400
= 100 gm of chocolate cookie dough
35% of chocolate cookie dough in one cup of Magic cookie dough
35% of 4 cups = 35/100 x 400
= 140 gm of chocolate cookie dough
therefore the dough Samantha has prepared has a total of 140 + 100 gm of chocolate cookie dough,
whereas total dough = 4 cups of magic cookie dough + 4 cups of supreme cookie dough = 8 cups
we assumed one cup will be 100 gm, therefore, 8 cups will be 800 gm
let the percentage of the chocolate cookie dough be x:
therefore, x/100 = 240/800
x = 240/800 x 100
x = 30
therefore, the percent of chocolate chips in the mixture is a total of 30%
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Kylie measured the length, x, of each of the insects she found underneath a
rock. She recorded the lengths in the table below.
Calculate an estimate of the mean length of the insects she found.
Give your answer in millimetres (mm).
Length (mm) Frequency
0≤x≤10 5
10 < x≤20 8
20≤x≤30 7
Answer: To estimate the mean length of the insects Kylie found, we can use the formula:
mean = (sum of (length * frequency)) / (sum of frequency)
We can calculate the sum of (length * frequency) by multiplying each length by its corresponding frequency and adding up the products. We can also calculate the sum of frequency by adding up all the frequencies. Using the table given, we have:
sum of (length * frequency) = (5 * 5) + (8 * 15) + (7 * 25) = 5 + 120 + 175 = 300
sum of frequency = 5 + 8 + 7 = 20
Substituting these values into the formula, we get:
mean = 300 / 20
= 15
Therefore, an estimate of the mean length of the insects Kylie found is 15 millimetres.
Step-by-step explanation:
5th grade math problem for my sister. Very confused on what it is asking. Assuming it’s 1/4
Answer:
5/8
Step-by-step explanation:
1/4*2 4/8
1/4*2 1/2
1/4*5/2
5/8
An empty container is a cylinder of radius 3.5 cm and height 40 cm
A tennis ball is a sphere of radius 3.5 cm
Will six of the tennis balls fit in the container?
Tick a box.
Yes
No
Show working to support your answer.
Pls help, thankyou
By addressing the posed question, we can get the following conclusion: Volume equation of six tennis balls = 6 179.59 1077.54 cm
Equation: What does it mean?In mathematics, an equations is a promise that two expressions are equivalent. Two sides that are divided by the algebraic symbol (=) make up an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is indeed the goal of equation solving. Equations can include one or more parts and be simple or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. A line is utilized in many different areas of mathematics, such as algebra, calculus, and geometry. We can calculate the volume of the container and the volume of one tennis ball, and then check if the volume of six tennis balls is less than or equal to the volume of the container.
Volume of container = πr2h
Volume of container = π[tex](3.5)^2[/tex](40) ≈ 1540.48 cm
Volume of one tennis ball = 4/3 π[tex]r^3[/tex]
Volume of one tennis ball = 4/3 π[tex](3.5)^3[/tex] ≈ 179.59 cm
Volume of six tennis balls = 6 × volume of one tennis ball
Volume of six tennis balls = 6 × 179.59 ≈ 1077.54 cm
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ERROR ANALYSIS Describe and correct the error in identifying the vertex, axis of symmetry, and
intercepts of the graph.
X
V
-2
A AY
6
8
Vertex: (1,
2
·N
xV
-8)
x-intercept: (-1,0) and (3,0)
y-intercept: (0, – 6)
axis of symmetry: y = 1
Corrected analysis of errors : Vertex: (-2, -8), x-intercepts: (-1,0) and (6,0), y-intercept: (0,-8), Axis of symmetry: x = -2
What are the errors?
There are multiple errors in the given analysis which are given below.
1. The x-coordinate of the vertex is incorrectly given as 1 instead of -2.
2. The y-coordinate of the vertex is incorrectly given as 8 instead of -8.
3. The x-coordinate of the axis of symmetry is incorrectly given as 1 instead of -2.
4. The given x-intercepts are incorrect. The correct x-intercepts are (-1,0) and (6,0).
5. The given y-intercept is incorrect. The correct y-intercept is (0,-8).
Corrected analysis:
Vertex: (-2, -8)
x-intercepts: (-1,0) and (6,0)
y-intercept: (0,-8)
Axis of symmetry: x = -2
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PLEASE HELP DUE RIGHT NOW
Question 1(Multiple Choice Worth 5 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
The second table is the one which represents a linear function.
What is a linear function?In mathematics, the terms "linear function" refer to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.
⇒ The first table does not represent a linear function because for two different values of x, there is same value for y.
⇒ The second table represents the linear function as it forms a straight line on the graph.
⇒ The third table does not represent a linear function because it does not have a constant slope.
⇒ The last table does not represent a linear function because it does not have a constant slope.
Hence, the second table represents a linear function.
As x is constant as 1, then all the y inputs will be in a straight vertical line
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Question: Which of the following tables represents a linear function?
A. x | −4 −1 0 1 2
y | −4 2 −4 0 2
B. x | 1 1 1 1 1
y | −3 −2 −1 0 1
C. x | −6 −1 0 2 3
y | −7 [tex]\frac{-16}{3}[/tex] −5 [tex]\frac{-13}{3}[/tex] −4
D. x | −2 −1 0 2 4
y | −4 [tex]\frac{-2}{3}[/tex] −1 [tex]\frac{2}{3}[/tex] 1
Cose measures her Frisbee and calculates that it has a circumference of 18.84 inches. What
s the Frisbee's radius?
Use 3.14 for . If necessary, round your answer to the nearest hundredth.
inches
As a result, the Frisbee's radius is 3 inches (rounded to the nearest hundredth) .
Set a radius?The distance from a circle's center to any point along its perimeter is known as the radius of a circle. It's typically indicated by "R" or "r" .
Describe circumference?The distance around a circle's periphery is its circumference. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.
C = 2πr, where C is the circumference and r is the radius, is the formula for calculating a circle's circumference.
This formula is rearranged to give us r = C /π 2 .
In this instance, we are aware that the Frisbee's circumference is 18.84 inches.
As a result, the radius can be determined using the formula r = C / 2π:
r = 18.84 / (2 * 3.14)
r = 18.84 / 6.28
r = 3
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cholesterol levels among fourteen-year-old boys are roughly normal, with mean 170 and standard deviation 30 milligrams per deciliter (mg/dl). you choose an srs of 4 fourteen-year-old boys and average their cholesterol levels. if you do this many times, the standard deviation of all the average cholesterol levels you get will be close to
The standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.
The standard deviation of the average cholesterol levels will be given by the standard error of the mean, which is calculated as
standard error of the mean = standard deviation / sqrt(sample size)
In this case, the sample size is 4, so we have
standard error of the mean = 30 / sqrt(4) = 15
Therefore, if we take many samples of 4 fourteen-year-old boys and average their cholesterol levels, the standard deviation of all the average cholesterol levels we get will be close to 15 mg/dl.
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Huw wants to open a savings account.
Here are the details of savings accounts advertised by two local Welsh banks.
Banc Padarn
Nominal interest rate of 1.98%
per annum
Interest paid monthly
Banc Teilo
AER 1-99%
Which of these two banks should Huw choose in order to gain the most interest per
annum?
As a result, Bank Padarn's AER is 2.0186%. This shows that Bank Padarn gives a greater interest rate when compared to the AER provided by Banc Teilo (1.9%).
What's the interest rate right now?A benchmark 30-year fixed mortgage's current average interest rate is 6.91% as of today, Tuesdays, March 21, 2023, a decrease of 3 basis points from seven days ago. If you're looking to refinance your mortgage, the current average 30-year fixed interest rate of 6.93%, which has been constant over the past week.
We must convert a nominal rate provided by Bank Padarn to the an AER in order to contrast the two rates.
AER is calculated as (1 + r/n)n - 1 where r is just the nominal rate of return & n is the annual frequency of interest payments.
r = 1.98% and n = 12 for Banc Padarn (since interest is paid monthly). The algorithm yields the following results when we enter these values: AER Equals (1 + 0.0198/12)12 - 1 ≈ 0.020186 = 2.0186%
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In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
The stem-and-leaf plot that correctly graphs the data set {15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5} is given as follows:
0| 0 5
1| 1 5 5 5
2| 0 0 0 0 3 6
3| 1 4 9 9
Key 1|1 = 11
What is shown by a stem-and-leaf plot?A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.
In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.
For example, as the team scored 20 points four times, we have the following observation:
2| 0 0 0 0
(one leaf of zero for each time, with the stem of 2).
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Sam has a deck that is shaped like a triangle with a base of 15 feet and a height of 6 feet. He plans to build a 4:5 scaled version of the deck next to his horse's water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)
Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
The area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.
The area of the new deck is 64% of the area of the original deck.
What is a triangle?
A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane. It is one of the basic shapes in geometry and is characterized by its three sides, three angles, and three vertices.
Part A:
The original deck has a base of 15 feet and a height of 6 feet. To create a 4:5 scaled version of the deck, we can multiply the base and height by the scale factor of 4/5:
New base = 15 * 4/5 = 12 feet
New height = 6 * 4/5 = 4.8 feet
Therefore, the dimensions of the new deck are 12 feet for the base and 4.8 feet for the height.
Part B:
The area of the original deck can be calculated using the formula for the area of a triangle:
Area of original deck = 1/2 * base * height = 1/2 * 15 * 6 = 45 square feet
The area of the new deck can be calculated in the same way, using the new dimensions:
Area of new deck = 1/2 * new base * new height = 1/2 * 12 * 4.8 = 28.8 square feet
Therefore, the area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.
Part C:
The ratio of the areas can be calculated by dividing the area of the new deck by the area of the original deck:
Area ratio = Area of new deck / Area of original deck = 28.8 / 45 = 0.64
The scale factor is 4/5, which is equal to 0.8. Therefore, we can compare the ratio of the areas to the scale factor to see if they are equivalent:
Area ratio / Scale factor = 0.64 / 0.8 = 0.8
Since the result is equal to the scale factor, we can conclude that the ratio of the areas and the scale factor are equivalent. This means that the area of the new deck is 64% of the area of the original deck.
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I need the awnser for this it’s due in 14 minutes
An equation for the line of best fit is y = 5x.
The y-intercept of the line of best fit is equal to (0, 0).
The size of a store which Feline Delights could expect to sell 20 bags per day is 4,000 square footage.
Feline Delights could expect to sell 20 bags per day in an 11,000 square foot store.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (45 - 30)/(9 - 6)
Slope (m) = 15/3
Slope (m) = 5
At data point (6, 30), a linear equation in slope-intercept form for this line can be calculated as follows:
y - y₁ = m(x - x₁)
y - 30 = 5(x - 6)
y = 5x - 30 + 30
y = 5x
When y = 20, the store size is given by;
20 = 5x
x = 20/5 = 4
In thousands, we have:
x = 4,000 square footage.
When x = 11,000 square footage, the number of bags is given by;
y = 5x
y = 5(11)
y = 55 bags.
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Suppose it takes John 40 minutes to run 4 miles. How long would it take him to run 9 kilometers? Round your answer to the nearest minute
John can run 4 miles in 40 minutes, so running 9 kilometers would take him approximately 56 minutes.
We're given that John can run 4 miles in 40 minutes. To find out how long it would take him to run 9 kilometers, we need to first convert 4 miles to kilometers.
One mile is equal to 1.60934 kilometers, so 4 miles is equal to 6.43736 kilometers (rounded to five decimal places).
Next, we can use the formula for speed:
Speed = Distance / Time
To solve for John's speed, we divide the distance he covered (6.43736 kilometers) by the time it took him to cover that distance (40 minutes):
Speed = 6.43736 km / 40 min ≈ 0.160935 km/min
Now we can use this speed to determine how long it would take John to run 9 kilometers. We can use the same formula as before, but this time we'll be solving for time:
Time = Distance / Speed
Substituting in the values we know:
Time = 9 km / 0.160935 km/min ≈ 55.8627 min
Rounding this answer to the nearest minute, we get:
Time ≈ 56 min
Therefore, it would take John approximately 56 minutes to run 9 kilometers.
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use the law of sines to find the missing side of the triangle
Using the law of sine, the missing side of the triangle is approximately 4.01 units.
The law of sines states that for any triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively
a / sin(A) = b/sin(B) = c / sin(C)
Using this law, we can find the missing side b as follows:
b/sin(B) = c/sin(C)
Since angle B and angle C are complementary, we can find angle C as:
C = 180 - A - B = 180 - 58 - 48 = 74 degrees
Now we have
b/sin(48) = 5/sin(74)
Solving for b, we get
b = (5 x sin(48))/sin(74) ≈ 4.01 units
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The given question is incomplete, the complete question is;
use the law of sines to find the missing side of the triangle
Identify the proof to show that △WZY≅△YXW , where WZ⊥ZY , WX⊥XY , ∠ZYW≅∠XWY , WX≅ZY , and WZ≅XY
Answer: To show that △WZY ≅ △YXW, we need to show that they are congruent by proving that all corresponding sides and angles are equal.
Given:
WZ⊥ZY and WX⊥XY, which implies ∠WZY = ∠YXW = 90°
∠ZYW ≅ ∠XWY (given)
WX ≅ ZY and WZ ≅ XY (given)
To prove:
△WZY ≅ △YXW
Proof:
By the given information, ∠WZY = ∠YXW = 90°.
By the given information, ∠ZYW ≅ ∠XWY.
Therefore, ∠WZY + ∠ZYW ≅ ∠YXW + ∠XWY. Combining these angles gives us ∠WZY + ∠ZYW = ∠YXW + ∠XWY.
Since the sum of interior angles in a triangle is 180°, we have:
∠WZY + ∠ZYW + ∠YZW = 180° for △WZY
∠YXW + ∠XWY + ∠YWX = 180° for △YXW
Substituting in the angle congruence (∠ZYW ≅ ∠XWY), we have:
∠WZY + ∠XWY + ∠YZW = 180° for △WZY
∠YXW + ∠ZYW + ∠YWX = 180° for △YXW
By the given information, WX ≅ ZY and WZ ≅ XY.
Therefore, by the Side-Angle-Side (SAS) congruence postulate, △WZY ≅ △YXW.
Hence, we have proved that △WZY ≅ △YXW.
Step-by-step explanation:
Suppose another team of researchers in 2009 believed that the rate of encounters in which the
whale comes within 3,281 feet of the bow in the lower bay sub-region of Glacier Bay was higher
than 20%. This team observed a sample of 85 encounters between cruise ships and whales in the
lower bay: the whale came within 3.281 feet of the bow in 25 of these encounters.
What will the standard deviation be???
The standard deviation of the normally distributed variable is given as follows:
s = 0.0434.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The mean this problem is given as follows:
[tex]\mu = p = 0.2[/tex]
Considering a sample size of 85, the standard deviation is given as follows:
s = sqrt(0.2 x 0.8/85)
s = 0.0434.
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at midnight the temperature was -8f. at noon, the temperature was 23f. which expression represents the increase in temperature?
A. -8 - 23
B. |-8| - 23
C. -8 - |23|
D. |-8 - 23|
Answer:
D
Step-by-step explanation:
23 - (-8)
23 + 8 = 31°
The temperature rose 31 degrees.
l-8 -23l = l-31l = 31 Absolute value is asking the distance from zero.
Helping in the name of Jesus.
Select the correct answer. What is the domain of the exponential function shown in the graph? The graph of the exponential function f(x) = -2^(-x+1)-1 flipped over the x and y axis. It passes through points (0,-6) and (1,-3) with a horizontal asymptote at y = 1.
The domain of the given exponential function is also all real numbers. We can calculate it in the following manner.
The given exponential function is obtained by taking the negative of the original function f(x) = 2^(-x+1) and then subtracting 1 from it. Since the original function has a horizontal asymptote at y=0 and the given function has a horizontal asymptote at y=1, we need to flip the graph of the given function over the x-axis to obtain the graph of the original function.
The point (0, -6) on the given graph corresponds to the point (0, 5) on the graph of the original function, and the point (1, -3) on the given graph corresponds to the point (1, 2) on the graph of the original function.
The general form of an exponential function is f(x) = a^x, where "a" is a positive constant. In this case, we have f(x) = 2^(-x+1), so "a" is equal to 2^1 = 2.
Since "a" is positive, the domain of the function is all real numbers. Therefore, the domain of the given exponential function is also all real numbers.
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Inez is taking a bicycling trip across the United States. Her destination is 3,280 miles away. If Inez travels 80 miles per day, how far does she have left to travel after 25 days of bicycling?
Answer: The distance left after 25 days is 1280 miles
Step-by-step explanation:
To calculate the distance, we use the formula:
[tex]s=\dfrac{d}{t}[/tex]
where,
s = speed of the bicycle = 80 miles/day
t = time taken = 25 days
d = distance travelled = ? miles
Putting values in above equation, we get:
[tex]\text{d}=(80 \ \text{miles}/\text{day} \times 25 \ \text{days})=2000 \ \text{miles}[/tex]
Total distance to the destination = 3280 miles
Distance traveled in 25 days = 2000 miles
Distance left after 25 days = [3280 - 2000] = 1280 miles
Hence, the distance left after 25 days is 1280 miles
The point W(-2, 6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, W'?
(2, -6)
When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate
So resulting point W' = (-(-2), -6) = (2, -6)
Answer:
(2, -6)
Step-by-step explanation:
When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate
So resulting point W' = (-(-2), -6) = (2, -6)
HELP 34 PONITS
6. Fill in the blanks within the area model for (5d - 12)(3d + 1) and then put a
check next to the answer you'll get after simplifying (combining like terms).
The answer to the simplified expression is option D. 15d^2 - 31d - 12
What is expansion by grid method?Expansion is the process of multiplying a given set of terms in a bracket with other terms in another bracket. It can be done using the grid method of expansion.
Considering the given question to fill the blanks, we have;
3d + 1
5d 15d^2 5d
-12 -36d -12
Thus, adding the terms one to another gives;
15d^2 + 5d - 36d - 12
15d^2 -31d - 12
The correct answer after simplifying the expression is: 15d^2 -31d - 12. Thus option D.
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For these equations of straight lines in the form y = mx + c, write down the value of m and c.
(i) y = 3x - 4
(ii) y = -3x + 7.
Answer:
see explanation
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 )
(i)
y = 3x - 4
with slope m = 3 and y- intercept c = - 4
(ii)
y = - 3x + 7
with slope m = - 3 and y- intercept c = 7
Answer:
here we can see clearly,
y = mx+c is the formulay= 3x+4answer: m = 3 c = 4 y= -3x + 7 answer: m = -3 c = 7