Answer:
p which is the y axis is -1
if a₁=3 and aₙ=5aₙ-₁ then find the value of a₅
Answer:
The value of a₅ is 1875.
Step-by-step explanation:
Given:
a₁ = 3
aₙ = 5aₙ₋₁
To find the value of a₅, we can apply the recursive formula to compute each term successively:
Step 1: Compute a₂
a₂ = 5a₁ = 5(3) = 15
Step 2: Compute a₃
a₃ = 5a₂ = 5(15) = 75
Step 3: Compute a₄
a₄ = 5a₃ = 5(75) = 375
Step 4: Compute a₅
a₅ = 5a₄ = 5(375) = 1875
An athlete runs 3 mi in 24 min. Is the rate of this athlete greater than, less than, or equal to the rate of an athlete who runs 4 mi in 33 min?
Answer:
the 3 / 24 athlete runs faster than the 4 /33 athlete
Step-by-step explanation:
3 / 24 = 0.125 mi per min
4 / 33 = 0.12121212121 mi per min
Find area of trapezium with height 8cm and the sum of its parallel sides as 15cm
Answer:
The Area of the trapezium is [tex]60cm^2[/tex]
Step-by-step explanation:
Given,
Height (h)= 8cm
Sum of the parallel sides (a+b)= 15cm
Area of trapezium = [tex]1/2*h*(a+b)[/tex]
=[tex]1/2*8*15[/tex]
=[tex]4*15[/tex]
Area of trapezium=60cm^2
Answer: Area = 60 cm²
Step-by-step explanation:
To find the area of a trapezium we use the formula
Area of trapezium = 1/2 (sum of parallel sides) × height
∴ Area = 1/2 ×15 cm × 8 cm
= 60 cm²
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What is the meaning of "∀X, Y ∈ A(X ⊂ Y ⇐ ⇒ f(X) ⊂ f(Y ))"?
GEOMETRY 100 POINTS CHALLENGE
Answer:
x = 10
Step-by-step explanation:
The diagonals of a rectangle are equal in length and bisect each other
⇒ JL = KM and
JN = LN = KN =MN
ΔJMN is an isosceles triangle since JN = MN
This means that the angles opposite to equal sides are equal
⇒ ∠JMN = ∠MJN
⇒ 7x - 2 = 3x + 38
⇒ 7x - 3x = 38 + 2
⇒ 4x = 40
⇒ x = 10
MY LAST QUESTION
an amusement park is comparing guest attendance for the months of june and august on the first day of each month, the park's attendance is 2,000 guests the attendance in june increases by 10% each day. the attendance in august decreases by 10% each day
PLS HELP :))
The park's attendance on the 30th day of June will be significantly higher than on the 31st day of August.
The amusement park in question has a starting attendance of 2000 guests on the first day of both June and August.
The park's attendance in June increases by 10% each day, while its attendance in August decreases by 10% each day.
The rate of change of the attendance in June and August can be calculated as follows:
Let's assume the attendance on the first day in June is equal to A.
Therefore, the attendance in June can be calculated as follows: On the 2nd day, the attendance would be 1.1A.
On the 3rd day, the attendance would be 1.1 × 1.1A = 1.21A
On the 4th day, the attendance would be 1.1 × 1.1 × 1.1A = 1.331A
And so on, until the 30th day of June.A = 2000
Therefore, on the 30th day of June, the attendance will be equal to:
Attendance on the 30th day = 2000 × 1.1^29 = 20,062.46 guests (rounded to the nearest whole number)
The attendance in August can be calculated in the same way, except that the rate of change will be negative (i.e., a decrease of 10% per day):
Attendance on the 2nd day = 0.9A
Attendance on the 3rd day = 0.9 × 0.9A = 0.81A
Attendance on the 4th day = 0.9 × 0.9 × 0.9A = 0.729A
And so on, until the 31st day of August.A = 2000
Therefore, on the 31st day of August, the attendance will be equal to: Attendance on the 31st day = 2000 × 0.9^30 = 49.28 guests (rounded to the nearest whole number)
Therefore, the park's attendance on the 30th day of June will be significantly higher than on the 31st day of August.
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Hakim drew an orange line that was 5/6 of an inch long. Then he drew a green line that was 1/6 of an inch long. How much longer was the orange line than the green line?
Answer:
4/6
Step-by-step explanation:
Here,
length of orange line (a): 5/6in
length of green line (b): 1/6in
Now,
a-b
=5/6-1/6
=5-1/6
=4/6in
.·.The orange line was 4/6in longer than the green line
On solving the provided question, we can say that - The orange line is 0.6 inches longer than the green line.
How do lines work?One-dimensional figures with length but no breadth are called lines.
You may write the length of the orange line as W and the length of the green line as I.
The orange line measures 5/6 of a meter, hence I = 5/6 = 0.83 or 0.8.The green line is supposed to be 1/6 long, hence W = 1/6 = 0.16 or 0.2.The formula for the length difference between the orange line and green lines is:
[tex]\text{I}-\text{W} = 0.8 - 0.2 = 0.6[/tex]
As a result, the orange line is 0.3 inches shorter than the green line.
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Which of the following crime scene search patterns should he use?
Factors such as scene size, complexity, evidence type, available resources, and time constraints determine the appropriate crime scene search pattern.
Determining the appropriate crime scene search pattern requires careful consideration of various factors to ensure a systematic and thorough search. While I cannot provide a calculation for this question since it involves subjective decision-making, I can provide a detailed explanation of the factors that should be taken into account when selecting a search pattern.
1. Size and nature of the crime scene: Consider the overall size and layout of the crime scene. Is it a small confined space or a large outdoor area? The size will influence the choice of search pattern. For smaller scenes, a line or grid search may be more suitable, while larger scenes may require a quadrant or zone search.
2. Type of evidence and scene complexity: Evaluate the type of evidence that may be present and the complexity of the scene. Are there specific areas or items of interest that require a focused search? Does the scene have multiple levels or rooms? A spiral search may be effective for scenes with a well-defined center, while a quadrant search allows for targeted searches in specific areas.
3. Number of investigators available: Assess the number of investigators available for the search. Different search patterns require different levels of manpower. For example, a grid search may require more personnel compared to a line search. Consider the available resources and allocate personnel accordingly.
4. Time constraints and urgency: Consider the urgency of the search and any time constraints. If there is a need for a rapid search, a line or spiral search may be more efficient. However, if time permits, a more detailed and thorough search, such as a grid or quadrant search, can be implemented.
5. Expert opinion and experience: Seek input from experienced crime scene investigators or forensic experts who can provide valuable insights and recommendations based on their expertise and prior experiences.
Ultimately, the choice of search pattern should be based on a careful assessment of these factors, combined with the investigator's professional judgment and experience. The goal is to conduct a methodical and comprehensive search to ensure all relevant evidence is discovered and properly documented.
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The question probable may be:
What factors should be considered when determining the appropriate crime scene search pattern to use?
GEOMETRY CHALLENGE
Given rhombus ABCD find m<1
The measure of the angle <1 is 90 degrees. Option C
How to determine the angleFirst, we need to know the properties of a rhombus, we have;
All sides of a rhombus are equalDiagonals bisect each other at 90°Opposite sides are parallel in a rhombusOpposite angles are equal in a rhombus.Adjacent angles add up to 180°.Now, from the information given, we have that;
m<1 is at the point where the diagonals of the rhombus meet.
The diagonals are labelled
BD and AC
Hence, the measure of angle 1 is 90 degrees
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M. Complete the table below by estimating the given by rounding off to a whole number (2nd column), 1 significant figure (3rd colcumn) and 2 significant figures (4th column) Given 325.248 85-27 2875-24 978-005 29-01 Estimated value Estimated value by rounding of Estimated value by rounding by rounding off to to 2sf 1sf off to a whole number
The rounded off values for columns 2, 3 and 4 are are shown on the table
What is a significant figure?You should know that a significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
The given numbers are 325.248 85.27 2875.24 978.005 29,01
Representing these in columns we have
Column 1 column 2 column 3 column 4
( whole number) (1 sig, figure) (2 sig. figures)
325.248 325 300.000 330.000
85.27 85 90.00 85.00
2875.24 2875 3000.00 2900.00
29,01 29 30.00 29.00
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
En un laboratorio trabajan 150 personas y en 30 días se consigue
realizar 750 pruebas. ¿Cuántas pruebas se pueden realizar con 200 personas?
With 200 people, it is estimated that they can perform 1000 tests.
To solve this problem, we can use the concept of direct proportionality. Let's analyze the given information:
In the laboratory, there are 150 people who perform 750 tests in 30 days. We can set up a proportion to determine the relationship between the number of people and the number of tests:
150 people = 750 tests
200 people = x tests
Using the concept of direct proportionality, we can set up the following equation:
150/750 = 200/x
To solve for x, we can cross-multiply:
150x = 750 * 200
150x = 150,000
x = 150,000/150
x = 1000
Therefore, with 200 people, it is estimated that they can perform 1000 tests.
It is important to note that this estimation assumes that the productivity and efficiency of the people in the laboratory remain constant. In reality, other factors such as work distribution, coordination, and resource availability can also affect the number of tests that can be performed. Additionally, this estimation does not consider any time constraints or limitations on the laboratory's capacity.
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Note the translated questions is:
150 people work in a laboratory and in 30 days a
perform 750 tests. How many tests can be done with 200 people?
What imagien shows a reflection?
An image that shows a reflection include the following: A. shape B.
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
Generally speaking, all congruent geometric figure are reflections of one another. This ultimately implies that, the geometric figures that are reflections of shape 1 must be congruent to it and these include the following under a reflection over the x-axis:
shape B.
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Determine which set of side measurements could be used to form a triangle.
a. 12, 23, 7
b. 10, 7, 2
c. 8, 3, 11
d. 5, 11, 8
The sets of side measurements that can form a triangle are: c. 8, 3, 11
d. 5, 11, 8
To determine which set of side measurements could be used to form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's evaluate each set of side measurements:
a. 12, 23, 7
In this case, the sum of the lengths of the two shorter sides (12 and 7) is 19, which is less than the length of the longest side (23). Therefore, this set of side measurements cannot form a triangle.
b. 10, 7, 2
Here, the sum of the two shorter sides (10 and 2) is 12, which is greater than the length of the longest side (7). This set of side measurements also fails to satisfy the triangle inequality theorem and cannot form a triangle.
c. 8, 3, 11
The sum of the two shorter sides (8 and 3) is 11, which is greater than the length of the longest side (11). Therefore, this set of side measurements can form a triangle.
d. 5, 11, 8
In this case, the sum of the lengths of the two shorter sides (5 and 8) is 13, which is greater than the length of the longest side (11). Hence, this set of side measurements can also form a triangle.
In summary, the sets of side measurements that can form a triangle are:
c. 8, 3, 11
d. 5, 11, 8
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The number line below shows information
about a variable, m.
Select all of the following values that m
could take:
-2, 4, -3.5, 0, -5, -7
-5 -4 -3 -2 -1 0 1 2 3 4 5
m
From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5
To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".
Looking at the number line, we can see the following values:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
From this list, the values that "m" could take are:
-2, -3.5, 0, -5
These values are present on the number line, indicating that they are possible values for "m".
Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.
It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.
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GEOMETRY 100 POINTS CHALLENGE
Answer:
ML = 28
Step-by-step explanation:
By mid-segment formula, we have :
[tex]AB = \frac{ML+ JK}{2}\\ \\[/tex]
⇒ ML = 2AB - JK
= 2(31) - 34
= 62 - 34
ML = 28
Bennett Griffin and Chula Garza organized Cole Valley Book Store as a corporation; each contributed $71,500 cash to start the business and received 5,600 shares of common stock. The store completed its first year of operations on December 31, current year. On that date, the following financial items for the year were determined: December 31, current year, cash on hand and in the bank, $69,250; December 31, current year, amounts due from customers from sales of books, $43,500; unused portion of store and office equipment, $72,500; December 31, current year, amounts owed to publishers for books purchased, $12,400; one-year note payable to a local bank for $3,200. No dividends were declared or paid to the stockholders during the year.
Required:
Complete the following balance sheet as of the end of the current year. Some information has been given below.
What was the amount of net income for the year? (Hint: Use the retained earnings equation [Beginning Retained Earnings + Net Income − Dividends = Ending Retained Earnings] to solve for net income.)
he net income for the year is $16,550.
Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)
Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500
Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800
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-25 - 8 =
A. -33
B -17
C. 7
D 33
Answer:
The answer is D
Step-by-step explanation:
If you set a number line, go 8 times left, and you can get -33
What is the equation of the circle below?
Answer:
(x + 4)² + (y - 1)² = 25
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given (h, k ) = (- 4, 1 ) and r = 5 , then
(x - (- 4) )² + (y - 1)² = 5² , that is
(x + 4)² + (y - 1)² = 25
A bacteria culture initially contains 2000 bacteria and doubles every half hour.
Find the size of the baterial population after 100 minutes.
Find the size of the baterial population after 4 hours.
Andrea is buying some new shirts and sweaters. She she is able to buy 3 shirts and 2 sweaters for $114 or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost?
A shirt is priced at $16, and a sweater carries a price tag of $33.
To solve this problem, we can set up a system of equations based on the given information. Let's represent the cost of a shirt as 's' and the cost of a sweater as 'w'.
From the first statement, Andrea is able to buy 3 shirts and 2 sweaters for $114. We can express this as the equation:
3s + 2w = 114.
From the second statement, Andrea is able to buy 2 shirts and 4 sweaters for $164. We can express this as the equation:
2s + 4w = 164.
To solve this system of equations, we can use the method of substitution or elimination. Here, let's use the substitution method.
First, let's solve the first equation for 's':
3s + 2w = 114
3s = 114 - 2w
s = (114 - 2w)/3.
Now, substitute the expression for 's' in the second equation:
2((114 - 2w)/3) + 4w = 164
(228 - 4w)/3 + 4w = 164
228 - 4w + 12w = 492
8w = 492 - 228
8w = 264
w = 264/8
w = 33.
Now, substitute the value of 'w' into the first equation to find the value of 's':
3s + 2(33) = 114
3s + 66 = 114
3s = 114 - 66
3s = 48
s = 48/3
s = 16.
Therefore, a shirt costs $16, and a sweater costs $33.
In summary, based on the given information and the solution to the system of equations, the cost of a shirt is $16, and the cost of a sweater is $33.
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The x and y intercepts for the linear equation x – 2y = -8 is
Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
45% of 30 is 18% of what number?
Answer quickly and provide all the work for the answer :)
Hello!
45% of 30 = 18% of x
45% * 30 = 18% * x
13.5 = 0.18x
x = 13.5/0.18
x = 75
so 45% of 30 is 18% of 75
Please explain your answer to the question in the picture with steps.
What it says is that:OABC is a square.
Point B is located in the line with the equation y=-4x+5
Fine the surface area of square OABC
To find the surface area of square OABC, we calculate the side length using the coordinates of point B, resulting in 25/16 units.
To find the surface area of square OABC, we need to determine the length of one side of the square. Since point B lies on the line with the equation y = -4x + 5, we can use this information to find the coordinates of point B and then calculate the distance between points O and B to determine the side length.
First, we need to find the x-coordinate of point B. Since we know the equation of the line y = -4x + 5, we can substitute y = 0 (since point B lies on the x-axis) and solve for x:
0 = -4x + 5
4x = 5
x = 5/4
Therefore, the x-coordinate of point B is 5/4.
Next, we substitute this x-coordinate back into the equation y = -4x + 5 to find the y-coordinate of point B:
y = -4(5/4) + 5
y = -5 + 5
y = 0
So, the coordinates of point B are (5/4, 0).
Now, we can calculate the distance between points O and B using the distance formula:
Distance = [tex]\sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}[/tex]
= [tex]\sqrt{[(0 - 0)^2 + (5/4 - 0)^2]}[/tex]
= [tex]\sqrt{[(5/4)^2]}[/tex]
=[tex]\sqrt{ [25/16]}[/tex]
= 5/4
Since OABC is a square, all sides are equal in length. Therefore, the side length of square OABC is 5/4.
To find the surface area of the square, we use the formula:
Surface Area = [tex]Side Length^2[/tex]
=[tex](5/4)^2[/tex]
= 25/16
Therefore, the surface area of square OABC is 25/16 square units.
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The diagram shows EFG. Which term describes point H?
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Point H is the ortho-center of our given triangle and option c is the correct choice.
We have been given an image of a triangle. We are asked to find the term that describes point H.
We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.
We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.
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What is mPN⌢
68°
136°
34°
92°
Answer:
arc PN = 136°
Step-by-step explanation:
the inscribed angle PLN is half the measure of its intercepted arc PN
then PN is twice the inscribed angle PLN , that is
PN = 2 × 68° = 136°
Give me decimals please.
The cylindrical coordinates of the point (4, 3, -3) are (5, 36.87°, -3).
To convert the point (x, y, z) = (4, 3, -3) to cylindrical coordinates (r, θ, z), we need to determine the magnitude of the radial distance (r), the angle (θ), and the height (z).
Magnitude of the radial distance (r):
The radial distance (r) can be found using the formula: r = sqrt(x^2 + y^2).
Plugging in the values, we have:
r = [tex]\sqrt{(4^2 + 3^2)}[/tex]
= [tex]\sqrt{16 + 9}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
Angle (θ):
The angle (θ) can be found using the formula: θ = arctan(y / x).
Plugging in the values, we have:
θ = arctan(3 / 4)
To find the value of θ, we can use a calculator or trigonometric tables. In decimal form, we have:
θ ≈ 36.87°
Height (z):
The height (z) remains the same in cylindrical coordinates.
Putting it all together, the point (x, y, z) = (4, 3, -3) in cylindrical coordinates is represented as (r, θ, z) = (5, 36.87°, -3).
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4.a) A car consumes a gallon of petrol for every 30 km drive. The driver of the car set out on a journey of 420 km with 10 gallons of petrol in the fuel tank. i) How many more gallons of petrol will be needed to complete the journey? ii)find the cost of the petrol for the journey of 420km if a gallon of petrol cost GH¢5.50
i) 4 more gallons of petrol will be needed to complete the journey.
ii) The cost of the petrol for the 420 km journey is GH¢55.00.
i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.
Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):
Distance covered with 10 gallons = 10 * 30 = 300 km
To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:
Remaining distance = Total distance - Distance covered with available petrol
Remaining distance = 420 km - 300 km = 120 km
Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:
Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons
Therefore, the driver will need 4 more gallons of petrol to complete the journey.
ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.
Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:
Cost of petrol = Total gallons used * Cost per gallon
Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00
Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.
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PLEASE HELP THIS IS HARD
The Area of the shaded portion is: 72 square inches
What is the Area of the shaded region?The formula for the area of a triangle is given by the formula:
Area = ¹/₂ * base * height
Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.
Thus:
Area of larger triangle = ¹/₂ * 17 * 13 = 110.5 square inches
Area of smaller triangle = ¹/₂ * 11 * 7 = 38.5 square inches
Thus:
Area of shaded portion = 110.5 square inches - 38.5 square inches
Area of shaded portion = 72 square inches
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