To determine the measure of the unknown segment, it's essential to first gather information about the given problem, such as the context, any provided measurements, and any relationships between the segments or angles involved. Once you have this information, you can utilize relevant geometric principles and theorems to establish connections and solve for the unknown value.
For example, if the unknown segment is a side in a triangle, you may apply the Pythagorean theorem, triangle inequality theorem, or trigonometric functions such as sine, cosine, or tangent to calculate its length. If the unknown segment is part of a circle, you might use the properties of arcs, chords, or the circumference to determine its measure. In cases where the unknown segment is part of a polygon, you can consider properties like diagonals, perimeter, or area to derive its length.
After identifying the appropriate method and relationships, you can set up equations and solve for the unknown variable. To verify the solution, you can plug it back into the original problem to ensure it satisfies all given conditions. In conclusion, finding the measure of an unknown segment involves understanding the problem's context, applying relevant geometric concepts, and using mathematical techniques to solve for the desired value.
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Chandler earns $15.25 an hour as a hostess at a local restaurant. She
earns an additional $25 in tips each night from take-out orders.
Determine if this linear relationship is proportional. Explain.
No, this linear relationship is not proportional, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes
Proportional relationships are those wherein the ratio between the two portions being as compared stays constant, no matter the values of those quantities.
In this case, we're evaluating Chandler's earnings primarily based on her hourly wage and her hints from take-out orders.
But, the ratio between Chandler's hourly wage of $15.25 and her tips of $25 per night varies relying on the number of hours she works.
For example, if Chandler works for 2 hours, her total income could be $30.50 (2 x $15.25) + $25 = $55.50.
If she works for four hours, her total earnings would be $61 (4 x $15.25) + $25 = $86. In this example, the ratio among her hourly salary and tips adjustments as her income increase with more hours worked.
Therefore, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes, this linear relationship is not proportional.
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The value of a car is worth 40,000, and it declines by 3% every year. Which function best represents the the value of the hybrid car.
40000(0. 03)^t
40000(1. 03)^t
The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is [tex]40,000(0.97)^{t}[/tex]
The value of the car = 40,000
The value of car declines at the rate of 3% every year
function is represented as F(t)
F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]
P is principal amount value of the car which is 40,000
R is rate at which it declines every year which is 3%
t is no. of year
Putting all the values in the equation we get
F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]
F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]
F(t) = [tex]40000(0.97)^{t}[/tex]
The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .
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Use The Fundamental Theorem of Calculus, Part 2 to evaluate / - (13 – 12) dt.
The value of the integral [tex]\int -1^1 (13 - 12) dt[/tex] is 26.
How to evaluate the integral?To evaluate the integral [tex]\int-1^1 (13 - 12) dt[/tex] , we need to find an antiderivative of the integrand, which is simply:
∫ (13 - 12) dt = 13t - 12
Using this antiderivative, we can evaluate the definite integral by applying the theorem:
[tex]\int-1^1 (13 - 12) dt = [13t - 12]_{(-1)^1[/tex]
Evaluating this expression at the limits of integration (-1 and 1), we get:
[13(1) - 12] - [13(-1) - 12]
Simplifying, we get:
= 13 - 12 + 13 + 12
= 26
Therefore, the value of the integral [tex]\int-1^1 (13 - 12) dt[/tex] is 26.
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What is the value of 45 nickels as a decimal number ?
Answer:
2.25
Step-by-step explanation:
45 nickels
45*5=225
225 cents
2.25
The value of 45 nickels in decimal number can be 2.25.
In the decimal system, each digit's value depends on its position or place value within the number.
A nickel is worth 0.05 dollars.
To find the value of 45 nickels, multiply the number of nickels by the value of each nickel:
So, Value = Number of nickels × Value of each nickel
= 45 × 0.05
= 2.25
Therefore, the value of 45 nickels is $2.25 as a decimal number.
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The average weight of Carl, Carla, Carmen, Clark, and Cathy is 107.6 lb. Cathy weighs 115 lb. What is the average weight of the other four? Show your work.
Answer:
Step-by-step explanation:
Let's start by finding the total weight of all five people:
Total weight = Average weight x Number of people
Total weight = 107.6 x 5
Total weight = 538
We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:
Total weight of other four = Total weight - Cathy's weight
Total weight of other four = 538 - 115
Total weight of other four = 423
To find the average weight of the other four, we can divide the total weight of the other four by the number of people:
Average weight of other four = Total weight of other four / Number of people
Average weight of other four = 423 / 4
Average weight of other four = 105.75 lb
Therefore, the average weight of the other four is 105.75 lb.
1. bona drives tor 3 hours at 44mph. clare drives 144 mies in 4 hours. how
for would bena travel if she drove for 3 hours at the same speed os
claire
2. janet and andrew leave their home at the same time. janet has 60
milles to travel and drives at 40 mph. andrew have 80 miles to travel
and also drives at 40 mph
a) how long does janets journey take?
(b) how much longer does andrew spend driving than janeta
1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.
2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.
1) Bona speed is 44mph
Time taken by Bona is 3 hour
distance travelled by Claire is 144 miles
Time taken by Claire is 4 hour
Claire's speed = distance / time
Claire's speed = 144/4
Claire's speed = 36 mph
Distance travelled by Bona = speed × time
Distance travelled by Bona = 36 × 3
Distance travelled by Bona = 108 miles
2) Janet distance = 60 miles
Janet speed = 40 mph
Time taken by Janet = distance / speed
Time taken by Janet = 60/40
Time taken by Janet = 1.5 hour
Janet would take 1.5 hour to complete the journey
Andrew distance = 80 miles
Andrew speed = 40 mph
Time taken by Andrew = distance / speed
Time taken by Andrew = 80/40
Time taken by Andrew= 2 hour
Andrew spend half hour more driving than Janet.
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Answer the following questions regarding convergence of series. It is possible that the correct answer would be "cannot be determined". (a) Suppse that sum Ak is a convergent series with known sum L Bk a convergent series with known
k=1
sum M. If L < M, does this guarantee that ax < bx for all k > 1? If not, provide a counter example.
L < M, as 1 < 1.25.
a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.
(a) Given two convergent series Σa_k (with sum L) and Σb_k (with sum M) where k=1 to ∞, and L < M, we are asked if a_k < b_k for all k > 1. The answer is no, this is not guaranteed.
Counter example:
Consider the following two convergent series:
Series A: Σa_k, where a_1 = 1/2, a_2 = 1/4, a_3 = 1/8, ... (a geometric series with a common ratio of 1/2)
Series B: Σb_k, where b_1 = 1, b_2 = 1/8, b_3 = 1/16, ... (a geometric series with a common ratio of 1/2 starting from the second term)
Sum L for Series A:
L = a_1 / (1 - (1/2)) = 1
Sum M for Series B:
M = b_1 + (b_2 / (1 - (1/2))) = 1 + 1/4 = 1.25
In this case, L < M, as 1 < 1.25. However, a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.
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Find dy/dx. x =^9root (t) y = 9 - t dy/dx = _____
To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]
However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]
Now, we can use the chain rule again to find dy/dt:
y = 9 - t
dy/dt = -1
Finally, we can use the formula for the chain rule to find dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]
So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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a driveway consists of two rectangles one rectangle is 80 ft long and 15 ft wide the other is 30 ft long and 30 ft wide what is the area of the driveway
Answer: 2100 square feet
Step-by-step explanation:
To solve this question we must add the areas of the two rectangles.
area = length x width
Rect 1:
a = lw
= 80 x 15 = 1200 square feet
Rect 2:
a = lw
= 30 x 30 = 900 square feet
so in total, the driveway is 1200 + 900 = 2100 square feet
Answer:
To find the area of the driveway, we need to find the area of both rectangles and add them together.
The area of the first rectangle is:
80 ft x 15 ft = 1200 sq ft
The area of the second rectangle is:
30 ft x 30 ft = 900 sq ft
To find the total area of the driveway, we add the two areas together:
1200 sq ft + 900 sq ft = 2100 sq ft
Therefore, the area of the driveway is 2100 square feet.
A restaurant in Richmond, BC, lists the prices on its menus in fractions of a dollar. Three friends have lunch at the restaurant. Each of 3 friends orders a veggie mushroom cheddar burger for 11 % ( , with a glass of water to drink.
What was the total bill be fore taxes, in fractions of a dollar?
If each of the 3 friends orders a veggie mushroom cheddar burger for 11%, the cost of each burger would be:
11% of $1.00 = $0.11
Since the prices are listed in fractions of a dollar, we can express the cost of each burger as 11/100 of a dollar.
So, the total cost of 3 veggie mushroom cheddar burgers would be:
3 x 11/100 = 33/100 = $0.33
Assuming that the glass of water is free, the total bill before taxes would be $0.33 for the 3 burgers. However, it's important to note that this calculation is based on the assumption that the prices are listed in fractions of a dollar, which may not be the case. If the prices are listed in a different unit, the calculation would need to be adjusted accordingly.
Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are
4
44 apples and
5
55 bananas in his pantry.
What is
P(select an apple
)
P(select an apple)start text, P, left parenthesis, s, e, l, e, c, t, space, a, n, space, a, p, p, l, e, end text, right parenthesis?
If necessary, round your answer to
2
22 decimal places.
If Cam randomly selects a piece of fruit from his pantry, the probability of selecting an apple is 4/9 or 0.44.
To find the probability of selecting an apple, we need to divide the number of apples by the total number of fruits in Cam's pantry.
Total number of fruits = number of apples + number of bananas = 4 + 5 = 9
P(select an apple) = number of apples / total number of fruits = 4/9
So, the probability of selecting an apple is 4/9 or approximately 0.44 when rounded to two decimal places.
Therefore, the probability is 4/9 or 0.44.
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Complete question is:
Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 4 apples and 5 bananas in his pantry.
What is P(select an apple)?
If necessary, round your answer to 2 decimal places.
Qn in attachment
.
..
Answer: d
Step-by-step explanation:
Answer:
pls mrk me brainliest
Step-by-step explanation:
(￣(ｴ)￣)ﾉ
Which equation represents the volume of each cone?
The equation which represents the volume of each cone is as follows:
V = (1/3)πr²h
Explanation :
In this equation, "V" represents the volume of the cone, "r" represents the radius of the base, and "h" represents the height of the cone.
V represents the volume of the cone. Volume is a measure of the space occupied by an object, and in this case, it refers to the space inside the cone.
π (pi) is a mathematical constant approximately equal to 3.14159. It is used in calculations involving circles and spheres.
r represents the radius of the base of the cone. The radius is the distance from the center of the base to any point on its circumference. Squaring the radius, r², gives us the area of the base.
h represents the height of the cone. It is the perpendicular distance from the base to the vertex (top) of the cone.
When we multiply the area of the base (πr²) by the height (h) and divide the result by 3, we get the volume of the cone. The division by 3 is necessary because the volume of a cone is one-third the volume of a cylinder with the same base and height.
So, the equation V = (1/3)πr²h provides a way to calculate the volume of a cone based on its radius and height.
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23- Find unit vectors that satisfy the stated conditions (a) Oppositely directed to v = (3,-4 ) and half the length of v.
The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
How to find a unit vector that satisfies the given conditions?To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:
Find the length of vector v:
|v| = sqrt(3^2 + (-4)^2) = 5
Divide vector v by 2 to get a vector with half its length:
v/2 = (3/2, -2)
To get a vector that is oppositely directed to v, we can reverse the direction of v/2:
-(3/2, -2) = (-3/2, 2)
Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:
|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)
u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)
Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
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If the solutions to 4x² + 1 = 81 are tg√/5, what is the value of g?
9 =
PLEASE HELP
Answer: 2√5, -2√5
Step-by-step explanation:
I need help Plssplss
Answer: 9.33
Step-by-step explanation: if you add them up, it's 9.33
The base of a solid is the region in the first quadrant between the graph of y=2x
and the x-axis for 0≤x≤1. For the solid, each cross section perpendicular to the x-axis is a quarter circle with the corresponding circle’s center on the x-axis and one radius in the xy-plane. What is the volume of the solid?
The volume of the solid is A. [tex]\pi/3[/tex]
What is the volume of a solid?The volume of a solid in geometry signifies the space it occupies inside a three-dimensional area. It denotes how much content can fill up its inner region, and as usual, measured in units like cubic feet, meters, or centimeters.
Finding the measurement formula varies from shape to shape but commonly involves multiplying width, height, and length. Given that many sectors rely on this term, such as engineering, architecture, and physics, understanding the concept of the volume of a solid weighs significantly.
If we take a cross-section of (x,y)perpendicular to the x-axis, with width dx, now the cross-section is a quarter circle with radius y.
Thus, the volume of the cross-section, since y = 2x becomes: [tex]\pi x^2 dx[/tex]
Now, the volume of the solid when integrated becomes: [tex]\frac{\pi }{3}[/tex]
Option A is correct.
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what is the number of cans that can be packed in a certain carton? (1) the interior volume of this carton is 2,304 cubic inches. (2) the exterior of each can is 6 inches high and has a diameter of 4 inches.
The number of cans that can be packed in a certain carton has correct statement as, Statements (1) and (2) together are not sufficient, option E.
Data sufficiency refers to evaluating and analysing a collection of data to see if it is sufficient to respond to a certain query. They are intended to assess the candidate's capacity to connect the dots between each question and arrive at a conclusion.
The size of each can is not revealed in statement 1 at all.
The size of the container is not disclosed in statement 2 at all.
We obtain two situations when we take into account both assertions. Case A: If the box is 1 x 1 x 2304 (inches) in size, then there are no cans that will fit within the carton.
Case B: If the box is 10 x 10 x 23.04 (inches) in size, then the carton can hold more than 0 cans.
The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.
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Complete question:
What is the number of cans that can be packed in a certain carton?
(1) The interior volume of this carton is 2, 304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
A. johnny translated abcd 3 units to the right and 4 units up to a new position, efgh. draw and label efgh.
b. tom rotated abcd to a new position, ijkl, 90º clockwise about the origin, o. draw and label ijkl.
c. tony placed a smaller car, represented as mnop, on the coordinate plane. mnop is a dilation of abcd with its center at the origin and a scale factor of -0.5. draw and label mnop.
A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).
B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.
C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.
THIS IS FOR 20 POINTS
What is the value of a?
27.5
50
90
45
The measure of arc a must be 2 times measure of inscribed angle, which is 90 degrees.
What is arc?
In geometry, an arc is a segment of a circle's circumference. It is defined by two endpoints and all the points on the circle's circumference between them.
What is inscribed angle?
An inscribed angle is an angle formed by two chords in a circle that have a common endpoint.
According to given information:For any inscribed angle in a circle, the measure of the angle is always half the measure of the arc that it intercepts. This is known as the inscribed angle theorem.
So, if we have an inscribed angle with a measure of 45 degrees, then the measure of its corresponding arc would be 2 times that, which is 90 degrees.
Therefore, if the inscribed angle is associated with arc a, and the measure of the corresponding angle is 45 degrees, then we know that the measure of arc a must be 2 times that, which is 90 degrees.
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Which of the following Is closest to the volume of the shoebox?
How do you set up and solve?
Answer:
H
Step-by-step explanation:
You take each given side and multiply them all together
18.4 x 8.8 x 11 = approx 1782
Q1. Consider the following options for characters in setting a password:
.
.
Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Letters = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, V, W, X, Y, z}
Special characters = 1 *, &, $. #}
Compute the number of passwords possible that satisfy these conditions:
• Password must be of length 6.
Characters can be special characters, digits, or letters,
Characters may be repeated.
.
There are 4,096,000,000 possible passwords of length 6 using special characters, digits, and letters, with characters allowed to be repeated.
To compute the number of passwords possible with a length of 6 using digits, letters, and special characters, with characters allowed to be repeated, follow these steps:
1. Count the number of options for each character type:
- Digits: 10 (0-9)
- Letters: 26 (a-z)
- Special characters: 4 (*, &, $, #)
2. Combine the options for all character types:
Total options per character = 10 digits + 26 letters + 4 special characters = 40
3. Calculate the number of possible passwords:
Since characters may be repeated and the password has a length of 6, the number of possible passwords = 40^6 (40 options for each of the 6 character positions)
4. Calculate the result:
Number of possible passwords = 40^6 = 4,096,000,000
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which rule explains why these triangles are congruent
Answer:
It's ASA, AAS,
Step-by-step explanation:
AAS- If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.
ASA-The ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent.
What are the coordinates of the point on the directed line segment from (-3,-5) to (9,−8) that partitions the segment into a ratio of 2 to 1?
The coordinates of the point are (7,0).
How to solve for the coordinatesdistance from (-3,-5) to (x,y) = 2 * distance from (x,y) to (9,-8)
Using the distance formula, we can write this equation as:
√[(x - (-3))^2 + (y - (-5))^2] = 2 * √[(9 - x)^2 + (-8 - y)^2]
Simplifying this equation, we get:
[tex](x + 3)^2 + (y + 5)^2 = 4[(9 - x)^2 + (-8 - y)^2][/tex]
Expanding and simplifying further, we get:
[tex]17x + 16y = 119[/tex]
So the coordinates of the point on the directed line segment from (-3,-5) to (9,-8) that partitions the segment into a ratio of 2 to 1 are:
x = (119 - 16y)/17
y = any value (since we can choose any value of y and then calculate x using the equation above)
For example, if we choose y = 0, then we get:
x = (119 - 16(0))/17 = 7
So the coordinates of the point are (7,0).
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The distance from city a to city b is 256. 8 miles. The distance from city a to city c is 739. 4 miles how much farther is the trip to city c than the trip to city b
Answer:
482.6 mi
Step-by-step explanation:
a to b = 256.8 mi
a to c = 739.4 mi
(a to c) - (a to b) = 739.4 - 256.8 = 482.6 mi
The coach recorded the time it took 14 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:55, 7:20, 9:14, 6:21, 7:12, 7:34, 6:10, 9:15, 9:18. Use the data set to complete the frequency table. Then use the table to make a histogram
The histogram for the frequency table is illustrated below.
To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.
Here is the completed frequency table:
Time Frequency
6:10 1
6:21 1
6:55 1
7:12 1
7:20 1
7:34 1
8:15 1
9:01 1
9:14 1
9:15 1
9:18 1
9:23 2
As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.
To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.
As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.
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Please help me with this math
Answer:
mean decreases by 15
median stays the same
[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]
The value of the fraction is 3/-2
What is a fraction?A fraction can simply be described as the part of a whole variable, a whole number or a whole element.
The different types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
4/-2 - 3/-6
find the lowest common factor
12 - 3/-6
subtract the value, we get;
9/-6
Divide the values into simpler forms
3/-2
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For this problem, a table has been started for you based on the information given in the problem. use inductive reasoning to complete the table.
an electronics store finds that over a period of three months, sales of stereos decreased. in march, the store sold 325 stereos. in april, the store sold 280 stereos, and in may, the store sold 235 stereos.
month
stereos sold
march
325
april
280
may
235
june
july
august
incorrect feedback has been removed from the screen.
type your answers and then click or tap done.
make a conjecture about the number of stereos sold in june. fill in the blank text field 1
190
make a conjecture about the number of stereos sold in july.
make a conjecture about the number of stereos sold in august.
Using inductive reasoning, we can observe a pattern in the given data: the number of stereos sold decreases by 45 each month.
We can apply this pattern to make conjectures about the number of stereos sold in June, July, and August.
June: 235 (May's sales) - 45 = 190 stereos
July: 190 (June's sales) - 45 = 145 stereos
August: 145 (July's sales) - 45 = 100 stereos
So, the conjectures for the number of stereos sold are:
June: 190
July: 145
August: 100
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An egg is dropped from the roof of a building. The distance it falls varies directly with the square of the time it falls. It takes 1/2 second for the egg to fall eight feet, how long will it take the egg to fall 200 feet?
What does K equal? And how many seconds?
Answer:
16 seconds
Step-by-step explanation:
