Exactly one-year later,
(a) Mean of the ages will be 13 years and 3 months.
(b) Range of the ages will be same 2 years and 7 months.
Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.
New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;
So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.
Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.
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If a1 =9 and an n-1 +2 then find the value of a5
Given that a₁ = 9 and aₙ = aₙ₋₁ + 2 , we can find the value of a5 by repeatedly applying the recursive formula to find a₂, a₃, a₄, and a₅.Using this method, we get a₅ is 17.
The given sequence is not defined explicitly. However, we can use the recursive formula to find the value of a5.
a₁ = 9 and aₙ = aₙ₋₁ + 2 for n > 1
To find a₂, we use the recursive formula
a₂ = a₁ + 2 = 9 + 2 = 11
To find a₃, we use the recursive formula
a₃ = a₂ + 2 = 11 + 2 = 13
To find a₄, we use the recursive formula
a₄ = a₃ + 2 = 13 + 2 = 15
To find a5, we use the recursive formula
a₅ = a₄ + 2 = 15 + 2 = 17
Therefore, the value of a₅ is 17.
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Let H: X – Y be a mapping. The set Y is called the
Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.
In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.
The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.
It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.
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Carolyn is carpeting her front room.
Work out how much carpet she needs by working out the area.
She will also need skirting boards around the sides of the room. To measure the boards needed, calculate the perimeter.
Area:
Perimeter:
Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.
To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:
Area = length x width = 5 x 3 = 15 square units
To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:
Perimeter = 2(length + width) = 2(5 + 3) = 16 units
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An individual makes five annual deposits of $2000 in a savings account that
pays interest at a rate of 4% per year. One year after making the last deposit, the
interest rate changes to 6% per year. Five years after the last deposit, the accumulated
money is withdrawn from the account. How much is withdrawn?
could you solve this problem?
The total amount withdrawn from the account after five years is $24,927.38.
How do we calculate?The future value of a series of annual deposits of $2000) can be calculated using the following formula:
FV = [tex]PMT x (((1 + r)^n^-^ 1) / r)[/tex]
where FV = the future value, PMT= the payment amount = $2000 r = the interest rate per period = 4% n = the number of periods = 5
the interest rate and the number of periods are the same.
[tex]FV1 = $2000 x (((1 + 0.04)^5^-^ 1) / 0.04) = $11,025.52[/tex]
This is the amount that the deposits will grow to one year after the last deposit, at an interest rate of 4% per year.
We use compound interest:
FV = [tex]PV x (1 + r)^n[/tex]
we apply this formula with a present value of $11,025.52, an interest rate of 6%, and 4 periods, we get:
FV2 = [tex]$11,025.52 * (1 + 0.06)^4 = $13,901.86[/tex]
Therefore the total amount withdrawn = FV1 + FV2 = $11,025.52 + $13,901.86 = $24,927.38
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Find the lateral and total surface area round to the nearest hundredth if necessary
The lateral and total surface area of the prism are 1000 square feet and 1120 square feet.
How to determine the lateral and total surface area of a prismIn this problem we need to determine the lateral and total surface area of a prism with a triangular base. The lateral surface area is the sum of the areas of the three rectangles and the total surface area is the sum of the lateral surface area and the areas of the two triangles.
The area formulas for the triangle and the rectangle are, respectively:
Triangle:
A = s · √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
a, b, c - Sides, in feet.s - Semiperimeter, in feet.A - Area, in square feet.Rectangle:
A = w · h
Where:
w - Width, in feeth - Height, in feet.A - Area, in square feet.Now we proceed to determine each surface area:
Lateral surface area:
A = 2 · (20 ft) · (17 ft) + (20 ft) · (16 ft)
A = 1000 ft²
Total surface area:
s = 0.5 · (17 ft + 17 ft + 16 ft)
s = 25 ft
A = √[(25 ft) · (25 ft - 17 ft)² · (25 ft - 16 ft)] + 1000 ft²
A = 1120 ft²
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Solve the equation for the indicated variable
X= (simplify your answer)
B = (715x) / (h^2)
Step 1: Get rid of the denominator by multiplying both sides by h^2
(B)(h^2) = 715x
Step 2: Isolate x by dividing both sides by 715
(Bh^2) / 715 = x
Answer: x = Bh^2 / 715
Hope this helps!
To the nearest megawatt, what is the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010?
The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
The data for this question can be found in the following table:
Year Electricity Generated (Megawatts)
2007 4,353
2008 7,113
2009 9,403
2010 10,089
To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.
Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts
Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
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What did Maleuvre write about Gauguin's views on Polynesian women?
According to Jean-Claude Maleuvre's book "Museum Memories: History, Technology, Art," Gauguin's views on Polynesian women were complex and contradictory. On the one hand, he was fascinated by their exotic beauty and saw them as a source of artistic inspiration. On the other hand, he objectified and exoticized them, portraying them as primitive and sexually available. Gauguin's depictions of Polynesian women have been criticized as perpetuating colonialist stereotypes and promoting a Westernized gaze.
Write an equation that can be used to determine the angle measure, in degrees, of angle DBC. Let n represent the measure of angle DBC. Then determine the measure of n
An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.
The measure of n is equal to 23 degrees.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;
∠ABD + ∠DBC = 90
∠ABD + n = 90
67 + n = 90.
n = 90 - 67
n = 23°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 3.
The median is the best measure of center, and it equals 19.
An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 12.
First quartile (Q₁) = 17.
Median (Med) = 19.
Third quartile (Q₃) = 20.
Maximum (Max) = 24.
In conclusion, the best measure of center is the median and it is equal to 19.
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PROJECT: INSCRIBED POLYGONS
You've learned about the different parts of a circle, as well as regular polygons and their angle measures. You've also learned how to use a protractor to measure angles.
In this project, you will apply this knowledge to inscribe regular polygons in a circle. If a polygon is inscribed in a circle, all of its vertices touch the circle. Here is an example of an equilateral triangle inscribed in a circle.
OBJECTIVES
Inscribe regular polygons in circles using a protractor, compass, and straight edge.
Materials
pencil and paper
protractor
compass
straight edge
Encik Halim bought 108 lemons to sell at his grocery shop. He packed 3 lemons in small packets and sold at the price of RM6.80 per packet. If he made a total profit of RM88.20, calculate the price of each lemon bought by him.
Answer:
the price of each lemon bought by Encik Halim is RM1.45.
Step-by-step explanation:
Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.
Let's assume that the cost of each lemon bought by Encik Halim is x RM.
The total cost of 108 lemons would then be 108x RM.
Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.
We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:
Total cost = Total revenue - Profit
Total cost = RM244.80 - RM88.20
Total cost = RM156.60
We know that Encik Halim bought 108 lemons, so we can write:
Total cost = Number of lemons bought x Cost per lemon
RM156.60 = 108x
Therefore, the cost per lemon bought by Encik Halim is:
x = RM156.60/108
x = RM1.45
So the price of each lemon bought by Encik Halim is RM1.45.
The graph of f(x) = a × [tex]b^x[/tex] passes through (2,54) and (5,16).
What is the value of b?
The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.
Given the function of the graph is,
f(x) = a*bˣ
It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.
Substituting the point (2, 54) in the given function we get,
f(2) = 54
a*b² = 54 ..................... (i)
Substituting the point (5, 16) in the given function we get,
f(5) = 16
a*b⁵ = 16 ..................... (ii)
So dividing equation (ii) by equation (i) we get,
(a*b⁵)/(a*b²) = 16/54
b³ = 8/27
b³ = (2/3)³
b = 2/3
Hence the value of b is 2/3.
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Which statement is true about the system x - 3y = 5 and y = x - 7?
• (8, 1) is a solution to one equation but not the other one, so it is a solution to the system.
• (8, 1) is not a solution to either equation, so it is not a solution to the system.
• (8, 1) is a solution to one equation but not the other one, so it is not a solution to the system.
• (8, 1) is a solution to both equations, so it is a solution to the system.
The solution to the given equation is ( 8 , 1 )
Given data ,
To determine whether (8, 1) is a solution to the system, we need to check whether it satisfies both equations:
x - 3y = 5: 8 - 3(1) = 5, which is true
y = x - 7: 1 = 8 - 7, which is true
Since (8, 1) satisfies both equations, it is a solution to the system. Therefore, the correct answer is:
Hence , (8, 1) is a solution to both equations, so it is a solution to the system
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The table below represents a linear equation
Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
We have to given that;
The table below represents a linear equation.
Now, The equation of line is,
Take two points (- 1, 5) and (1, 9)
⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)
⇒ y - 5 = 4/2 (x + 1)
⇒ y - 5 = 2 (x+ 1)
⇒ y - 5 = 2x + 2
⇒ y = 2x + 7
Hence, By options,
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
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Find the approximate radius of a circle with a circumference of 23.21 feet. Use 3.14 for π
. Round to the nearest hundredth if necessary.
Thee radius of the circle is 3. 696 feet
How to determine the radiusThe formula that is used for calculating or determining the circumference of a circle is expressed as;
C = 2πr
Given that the parameters for the formula are expressed thus;
C is the circumferenceπ takes the constant value of 3.14r is the radius of the circleFrom the information given, we have that;
Radius = 23.21 feet
Substitute the values, we get;
23.21 = 2× 3.14r
Multiply the values
r = 23.21/6.28
Divide the values
r = 3. 696 feet
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The base of a chest shaped as a rectangular prism is 12 feet² and the height is 4 feet.
What is the volume?
Answer:
The answer is 576
Step-by-step explanation:
the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.
The area of a circle is 36π centimeters. What is the circumference of a circle in terms of π.
At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
According to the NOAA, the state of Oregon has just over 6 million feet of Pacific coastline. If the population of Oregon is approximately 3.8 million people, find the number of feet of coastline per capita in Oregon. Round your answer to the nearest hundredth
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
what is unitary method ?In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.
given
Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:
Total shoreline / Population equals coastline per person.
coastline divided by population (3,800,000) equals 6,000,000 feet.
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
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Help with this question please l need it
Answer:
(x+4)(x-9)!!!!!!!!!!!!!!!!!!
An airplane is heading north at an airspeed of 550 km/hr, but there is a wind blowing from the southwest at 40 km/hr.
The plane will end up flying
degrees off course
The plane's speed relative to the ground will be
km/hr
Answer: To end up due north, the pilot will need to fly the plane 3.382 degrees east of north.
Step-by-step explanation:
don't know how to explain got it form chegg
A toy car travels 12 centimeters per second ehich graph best best represents why the number of centimeters the toy var travels in x seconds
Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.
Step-by-step explanation:
Given: rectangle MNPQ ~ rectangle RSTU
- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU
The perimeter of rectangle RSTU is 21 cm.
The area of the rectangle RSTU is 27 cm².
How to find the perimeter and area of a rectangle?A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.
Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.
Hence,
Let's find the width of the rectangle MNPQ
14 = 2(4 + w)
14 = 8 + 2w
14 - 8 = 2w
2w = 6
w = 6 / 2
w = 3 cm
Therefore, using similar ratio,
4 / 6 = 3 / RU
cross multiply
4RU = 18
RU = 18 / 4
RU = 4.5 cm
Therefore,
Perimeter of the rectangle RSTU = 2(6 + 4.5)
Perimeter of the rectangle RSTU = 2(10.5)
Perimeter of the rectangle RSTU =21 cm
Area of the rectangle RSTU = 4.5 × 6
Area of the rectangle RSTU = 27 cm²
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 2 more hours to do homework than to shop online.
To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:
Videos: 10% of 40 hours = 4 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Shopping: 15% of 40 hours = 6 hours
To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 6 hours (shopping) = 2 hours
Therefore, Heracio used the computer 2 more hours to do homework than to shop online.
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4. The arithmetic mean of a data set is the measure of center is ….
A) that is found by adding the data values and dividing the total by the number of data values
B)that is the value midway between the maximum and minimum values in the original data set
C)that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
D) that is the value that occurs with the greatest frequency
The correct statement is A) that is found by adding the data values and dividing the total by the number of data values
What is meant by adding?
Adding is an operation in which two or more numbers or quantities are combined to obtain a sum. It is represented by the symbol "+" and is one of the four basic arithmetic operations.
What is meant by dividing?
Dividing is an operation that separates a quantity or a number into equal parts or groups. It is represented by the symbol "÷" or "/" and is one of the four basic arithmetic operations.
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Solve the radical equation.
√3x-2-√11+x= -1
Answer:
[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]
3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
4x^2 + 10 + x - 50 - x^2 + 4 + 11x
The factorization of the polynomial is determined as (x + 6)(x - 2).
What is the factorization of the polynomial?The factorization of the polynomial is calculated as follows;
4x² + 10 + x - 50 - x² + 4 + 11x
collecting similar terms, we will have;
3x² + 12x - 36
divide through by 3;
x² + 4x - 12
Factorize the expression as follows;
x² + 6x - 2x - 12
x (x + 6) - 2(x + 6)
(x + 6)(x - 2)
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Convert the decimal 15.75 into a percent.
The decimal 15.75 into a percentage is 1575%
How to convert the decimal into a percentageFrom the question, we have the following parameters that can be used in our computation:
Decimal = 15.75
This means that
Number = 15.75
Multiply the number by 1
so, we have the following representation
Number = 15.75 * 1
Express 1 as 100%
This gives
Number = 15.75 * 100%
Evaluate the products of 15.75 and 100
So, we have
Number = 1575%
Hence, the percentage is 1575%
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What is the area of one of the bases,b, of the prism b=_in2
Answer: 6
Step-by-step explanation:
Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².
Answer:
Step-by-step explanation:
B= area of the triangle 1+area of triangle 2
(1/2*3*1)+(1/2*2*1)
=1.5+1
=2.5