Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:
D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)
So, the position vector of point D is (3i + 0.5j - 0.5k).
(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).
The magnitude of this difference is given by:
|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4
So, we have:
√((a-2)^2 + 2^2 + 2^2) = 4
(a-2)^2 + 2^2 + 2^2 = 16
(a-2)^2 = 16 - 4 - 4
(a-2)^2 = 8
a-2 = ±2√2
Since a < 0, we have:
a = 2 - 2√2
So, the value of a is 2 - 2√2.
Step-by-step explanation:
During its first month of business, Dig the Dogs, Inc. purchased $900 of hotdogs of which it paid $300 and owes the rest. During the month, it sold 3/4 of its inventory for $1,000 on account. What is the amount of Cost of Goods Sold for the month ended?
Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.
Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory = 0 + 900 - 300 = $600 Therefore, the cost of goods sold for the month ended is $600.
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Ata school
number of boys : number of girls = 11: 9
There are 124 more boys than girls.
Work out the total number of students at the school.
The total number of students at the school is 1240.
What is Ratio ?
With the dividend or number being divided as the antecedent and the divisor or number that is dividing as the consequent, a ratio compares two quantities by division.
we know that, number of boys : number of girls = 11: 9
Let's assume the number of boys = 11x
and, the number of girls = 9x
similarly, There are 124 more boys than girls
So, number of boys = 124 + number of girls
11x = 124 + 9x
2x = 124
x = 62
So, number of boys = 11 ×62 = 682
number of girls = 9 × 62 = 558
∴ Total number of students is 1240 i.e.(682+558).
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The table shows the monthly revenue of a business rising exponentially since it opened an online store.
b. Write an equation to represent the revenue, R, as a function of months, m, since the online store opened.
The monthly revenue of the business grows by 8%, monthly.
The definition of revenue?
The total income a firm receives from the sale of products or services that are connected to its core business operations is referred to as revenue.
Since it appears at the top of the income statement, revenue, also known as gross sales, is frequently referred to as the "top line." An organization's whole earnings or profit is known as income, or net income.
An exponential function is represented as
y = abˣ
From the table we have the following ordered pair
(x,y) = {(0,72000) (3,90000)}
So, we have
90000 = 72000 * b³
Divide both sides by 72000
b³ = 1.25
Take the cube roots of both sides
b = ∛1.25
b = 1.08
Recall that
b = 1 +r
1 + r = 1.08
r = 0.08
r = 8%
Hence, the monthly revenue of the business grows by 8%, monthly.
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Pls show your work thank you will mark the Brainliest
Answer:
12.3
Step-by-step explanation:
take x=0 because intercept means cutting the y axis when x=o
Answer:
Step-by-step explanation:
7
U={ positive integer between 9 and 21} P={odd numbers} Given that P and Q are subsets of U a. List all the members of P, Q and U b. Illustrate the information on a Venn diagram c. Find P1 and Q1
The set of the numbers are all integers from 9 to 21 inclusive
What is a set?It is the collection of items to form a group
All the members of:
P={odd numbers}
P={9,11,13,15,17,19,21}
Q={Even numbers}
Q= {10,12,14,16,18,20}
U={ positive integer between 9 and 21}
This means that U = {9,10,11,12,13,14,15,16,17,18,19,20,21}
Therefore, P1 and Q1
P prime include all the elements in the universal set that are not in the subset P = {10,12,14,16,18,20}
and Q prime include all the elements in the universal set that are not in subset Q = P={9,11,13,15,17,19,21}
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What is the measure of the smallest angle?
(Image)
67°
69°
52°
61°
The measure of the smallest angle is 52 degrees
How to determine the measure of the smallest angle?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The triangle
The sum of angles in a triangle is 180
So, we have
2x + 3x - 11 + 2x + 9 = 180
Evaluate the like terms
7x = 182
So, we have
x = 26
This means that
2x = 2 * 26 = 52
3x - 11 = 3 * 26 - 11 = 67
Hence, the smallest is 52 degrees
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A submarine starts at the depth of -15 meters and then dives down 0.5 meter every second
The linear function representing the depth of the submarine after t seconds is given as follows:
d(t) = -15 - 0.5t.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = -15 -> initial depth of the submarine.m = -0.5 -> each second, the height decays by 0.5.Hence the function is given as follows:
d(t) = -15 - 0.5t.
Missing InformationThe problem asks for the linear function representing the depth of the submarine after t seconds.
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what can we conclude from the five number summary about the location of the 20th percentile? the 90th percentile?
By knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
The five number summary is a way to summarize the distribution of a set of data by providing information about its minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum. Using this summary, we can infer information about the location of specific percentiles.
For the 20th percentile, we can conclude that it lies between the minimum and the first quartile. The 20th percentile represents the value below which 20% of the data falls, so it must be less than or equal to the first quartile, which is the value below which 25% of the data falls. It must also be greater than or equal to the minimum.
For the 90th percentile, we can conclude that it lies between the third quartile and the maximum. The 90th percentile represents the value below which 90% of the data falls, so it must be less than or equal to the maximum, which is the largest value in the data set. It must also be greater than or equal to the third quartile, which is the value below which 75% of the data falls.
In conclusion, by knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
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Writing Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares.
Answer:
The length of the hypotenuse is 17.
How long will it take someone to knit a scarf that is 160 cm long?
If Pat can knit 2cm in 35 minutes, then would take Pat approximately 2800 minutes to knit a scarf that is 160cm long.
If Pat can knit 2cm in 35 minutes time
then she can knit 1cm in (35/2) minutes, or 17.5 minutes.
To determine the total time to knit a 160cm scarf
Pat would need to work a total of
160cm x 17.5 minutes/cm = 2800 minutes.
Hence,
It would take Pat approximately 2800 minutes to knit a scarf that is 160cm long. This is equivalent to about 46.7 hours or 1.94 days of work
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Pat is knitting a scarf . On average she can knit 2cm in 35mins. How long will take her to knit a scarf that is 160cm long?
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 3 AM.
The temperature at 3 AM is about 53 degrees Fahrenheit.
How would you define temperature?The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.
A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.
We are aware that a sinusoidal function models temperature, and the following information is crucial:
A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.
The day's average temperature is 60 degrees.
We're looking for the temperature at three in the morning, or three in 24-hour time.
We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:
B = 2π/24 = π/12
To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:
C = (8/24) * 2π = (1/3)π
To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:
A = 10
Finally, we can use the formula to find the temperature at 3 AM:
f(x) = A sin(B(x - C)) + D
f(3) = 10 sin(π/12(3 - (1/3)π)) + 60
f(3) ≈ 53.4
So the temperature at 3 AM is about 53 degrees Fahrenheit.
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Please find the missing side length using trig
Answer:
13.0898597466511 or 13.09
Step-by-step explanation:
pls help i dont know how to do it i've been out sick
A rectangle is divided up into four smaller rectangles/ The length of each segment is a whole number of cm. The areas of three rectangles is given in the diagram. Find the number of sq. cm in the total area of rectangle ACEG
The solution is, The value of N is 12 sq cm.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
1. Find the greatest common factor of 35 and 42 to find the length (horizontal). The GCF is 7.
2. The horizontal length of the 35 and 42 sq cm is 7, and the heights are 5 and 6 respectively.
3. Moving on tot he 10 sq cm rectangle,
since the height of just that one rectangle is and 10/5 is 2, the horizontal length is 2.
4. For n, the horizontal length is 2 and the height is 6.
2 X 6 is 12 sq cm.
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1. The volume of the cone is 27pi what is the volume of the cylinder
with the same radius and height
The height is 9 units
V = 763.407015 m
A survey was done that asked employees to indicate whether they ride a bicycle or drive to work, and whether they live up to 5 miles or more than 5 miles from work. What is the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle? Enter your answer, rounded to the nearest whole percent, in the box
The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :
From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:
P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)
= 35% x (20%/35%)
= 0.5714 or 57% (rounded to the nearest whole percent)
Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
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15. Find the perimeter.
11.8
13.3
7.5
11.9
Answer: 47.20cm
Step-by-step explanation:
Write the exponential function that describes the situation.
The initial amount of the function is 12, and then it decreases by a factor of 7/9
with each unit increase in x.
Please help thank you
The tension forces are 1895 N and 2542 N.
What is the tension in the ropes?
Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart
We know that the third angle in the triangle that is formed is;
180 - [35 + 48]
= 97 degrees
We then have the tension in the ropes as T1 and T2
Using the sine rule;
T1/sin 35 = 3275/sin97
sin97T1 = 3275 sin 35
T1 = 3275 sin 35/sin97
T1 = 1895 N
For T2
T2/sin48 = 3275/sin97
sin97T1 = 3275 sin 48
T1 = 3275 sin 48/sin97
T1 = 2542 N
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If Jimmy drove 300 miles at a rate of 50 miles per hour, find the number of hours Jimmy traveled.
Answer:
He drove 6 hours.
Step-by-step explanation:
distance = rate times time
300 = 50t Divide both sides by 50
t = 6
15 pts pls help me TvT
Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Let M be the midpoint of AB, so EM is perpendicular to AB.
Since OF is a diameter of the circle, angle EOF is a right angle.
Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.
The corresponding sides are proportional:
EF / EA = EO / EM.
EM is half the length of AB, which is the diameter of the semicircle,
EO must be equal to the radius of the semicircle.
Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,
EF = EA.
Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
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a plane contains 40 lines, no 2 of which are parallel. suppose that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, 6 points where exactly 6 lines intersect, and no points where more than 6 lines intersect. find the number of points where exactly 2 lines intersect.
With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.
In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".
Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.
The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.
To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:
2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6
Expanding the right side of the equation:
2x = 9 + 16 + 25 + 36
= 86
Dividing both sides of the equation by 2:
x = 43
So there are 43 points where exactly 2 lines intersect.
This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.
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draw an angle of 65° and draw an angle equal to this angle, using ruler and compass
The Construction of angle equal to 65 degree is shown below with attached figure.
What is Construction?Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructs.
The steps to draw angle 65 and copy of Angle:
(i) Draw ∠AOB = 65° with the help of protractor.
(ii) Draw a ray O’X.
(iii) With O as center and any radius, draw an arc cutting OA and OB at C and D respectively.
(iv) With O’ as center and with the same radius, draw an arc, cutting O’X at P.
(v) With P as center and radius equal to CD, cut the arc through P at Q.
(vi) Join O’Q and produce it to Y. Then ∠YO’X is the required angle equal to ∠AOB.
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if the mean is 9,8,10,x,14 is 11 then find the value of x
The value of x is 14
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
To find the mean, add up all the numbers and then divide by the number of numbers
(9+ 8+10+ x+14)/5 = 11
Multiply each side by 5
9+ 8+10+ x+14 = 55
Combine like terms
41 +x = 55
Subtract 41 from each side
x =14
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A researcher found that for the years 2011 to 2017, the equation y = -0. 25(x - 2)^2 + 16, models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. During what year was the average of couches sold in Germany the greatest?
The vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
The equation y = -0.25(x - 2)² + 16 models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. We can find the year when the average of couches sold in Germany was the greatest by finding the maximum value of the equation.
To find the maximum value, we can first rewrite the equation in vertex form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
y = -0.25(x - 2)² + 16
y = -0.25(x² - 4x + 4) + 16
y = -0.25x² + x + 15
To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where f(h) is the value of y at the vertex.
h = -b/2a = -1/(2*(-0.25)) = 2
k = f(h) = -0.25(2)² + 2 + 15 = 16
Therefore, the vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
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How to factorize and get the answer?
make brainalist keep smiling dude..!
In this figure, lines a and b intersect a transversal, c. What is the relationship between ∠1 and ∠5?
m∠1 = m∠5, because alternate exterior angles are congruent.
What are angles of parallel lines?Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.
Given:
lines a and b intersect a transversal, c.
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
m∠1 = m∠5 (Alternate exterior angles are congruent)
m∠1 = m∠5, because alternate exterior angles are congruent.
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The Complete Question is attached below.
What is the answer to 52+6y-22
Which of the following sequences are geometric?
Check all that apply.
Answer: A and C
Step-by-step explanation:
- Geometric sequences are sequences where there is a constant number being multiplied or divided.
- In A, we are dividing by 2 each time. In C, we are multiplying by 3
each time.
- B is not multiplication or division. Neither is D.
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Kathy is organizing her desktop, which measures 22 inches by 4 feet. What is the area of Kathy’s desktop?
The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
Kathy is organizing her desktop, which measures 22 inches by 4 feet. To calculate the area of Kathy’s desktop, we can use the formula for area, which is length multiplied by width. In this case, the length is 4 feet and the width is 22 inches. To make the measurements easier to work with, we can convert the length into inches. There are 12 inches in a foot, so 4 feet is equal to 48 inches. Now, the length of Kathy’s desktop is 48 inches and the width is 22 inches. To calculate the area, we multiply the length (48 inches) by the width (22 inches). The area of Kathy’s desktop is 1,056 square inches.
To further explain the concept of area, it is the amount of two-dimensional space that a shape takes up. It is measured in square units, such as square inches, square feet, or square yards. To calculate the area of any shape, you need to know its length and width. To calculate the area of a rectangle, you multiply the length by the width. The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
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