(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.
(a) For the series 1+2+3+4+...+392:
Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.
(b) For the series 1+2+3+4...x:
To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).
(c) For the series 546 + 547 + 548 + 549:
Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.
The final answer for each part is:
(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
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A marketing firm conducts a survey to determine the ages of their survey subjects who like a new health drink.
This is the resulting data from their survey:
49, 63, 78, 22, 41, 39, 75, 61, 63, 65,
58. 37. 45, 52, 81, 75, 78, 72, 68, 59,
72, 85, 63, 61, 75, 39, 41, 48, 59,55
61, 25, 61, 52, 58, 71, 75, 82, 49, 51
The mean age of the subjects who like the new health drink is (type your answer...)
and the median age of the subjects is (type your answer..)
Answer:
Mean = 59.1, Median = 61
(there might have been a mistake in calculation (a lot of numbers!))
Step-by-step explanation:
The sample size is 40,
Now, the formula for the mean is,
Mean = (sum of the sample values)/(sample size)
so we get,
[tex]Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1[/tex]
To find the median, we have to sort the list in ascending (or descending)order,
we get the list,
22,25,37,39,39,41,41,45,48,49,
49,51,52, 52,55,58, 58, 59, 59, 61,
61, 61, 61, 63, 63, 63, 65, 68, 71, 72,
72, 75, 75, 75, 75, 78, 78, 81, 82, 85
Now, we have to find the median,
since there are 40 values, we divide by 2 to get, 40/2 = 20
now, to find the median, we takethe average of the values above and below this value,
[tex]Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value[/tex]
And the (n+1)th value is the 21st value
Now,
The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,
Median = (61+61)/2
Median = 61
Find the length of KL.
Answer:
KL = 6
Step-by-step explanation:
We see that the length of IL includes IJ, JK, and Kl and is 26.
Since IL = 26 and IJ + JK + KL = IL, we can subtract the sum of the lengths of IJ and Jk from IL to find KL:
IL = IJ + JK + KL
26 = 9 + 11 + KL
26 = 20 + KL
6 = KL
Thus, the length of KL is 6.
We can confirm this fact by plugging in 6 for KL and checking that we get 26 on both sides of the equation when simplifying:
IL = IJ + JK + KL
26 = 9 + 11 + 6
26 = 20 + 6
26 = 26
Thus, our answer is correct.
PLEASE HELP ITS HARD
Answer:
- 8a²
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m - n)}[/tex]
given
[tex]\frac{80a^9}{-10a^7}[/tex]
= [tex]\frac{80}{-10}[/tex] × [tex]a^{(9-7)}[/tex]
= - 8 × a²
= - 8a²
What is the average rate of change in f(x) on the interval [5,9]?
A)-1.5
B)6/4
C)4
D)-6
Answer:
A) -1.5
Step-by-step explanation:
We can find the average rate of change of a function over an interval using the formula:
(f(x2) - f(x1)) / (x2 - x1), where
(x2, f(x2)) is the rightmost part of the interval. In this problem, 9 is our x2 and f(x2) is 3 since 3 is the y-coordinate when you plug in 9 for f(x))(x1, f(x1)) is the leftmost part of the interval of the interval.In this case, 5 is our x1 and f(x1) is 9 since 9 is the y-coordinate when you plug in 5 for f(x).Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].
(3 - 9) / (9 - 5)
(-6) / (4)
-3/2
is -3/2.
If we convert -3/2 into a normal number, we get -1.5
Thus, the average rate of change in f(x) on the interval [5,9] is -1.5
Answer:
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.
From inspection of the given graph:
f(5) = 9f(9) = 3Substitute the values into the formula:
[tex]\textsf{Average rate of change}=\dfrac{f(9)-f(5)}{9-5}=\dfrac{3-9}{9-5}=\dfrac{-6}{4}=-1.5[/tex]
Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.
What is the value of x in equation 2/3(1/2x+12)=1/2(1/3x+14)-3
Answer:
x=-24
Step-by-step explanation:
2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)
GEOMETRY 40POINTS
TY
Answer:
It's 7.81
Step-by-step explanation:
Find the area of the region bounded by the graphs of f(x) = x^3 + x^2 - 6x and g(x) = 2x - x^2
The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.
To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.
First, let's find the points of intersection by setting f(x) equal to g(x):
[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]
Rearranging the equation, we get:
[tex]x^3 + 2x^2 - 8x = 0[/tex]
Factoring out an x, we have:
[tex]x(x^2 + 2x - 8) = 0[/tex]
Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).
To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:
Area = ∫[from -4 to 2] (f(x) - g(x)) dx
Evaluating the definite integral, we have:
Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx
= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx
Integrating each term and evaluating the integral, we find:
Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2
= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]
= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]
= 1/3 + 128/3 - 16 + 4 - 128/3 + 64
= 1/3 + 4 + 64
= 69 1/3
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Help I’m lost somebody please help me
Answer:
l
Step-by-step explanation:
The table represents a logarithmic function f(x).
1 over 125 −3
1 over 25 −2
one fifth −1
1 0
5 1
25 2
125 3
Use the description and table to graph the function, and determine the domain and range of f(x). Represent the domain and range with inequality notation, interval notation, or set-builder notation. Explain your reasoning.
The graph of the logarithmic function f(x) exhibits an increasing trend as x approaches positive infinity, while it approaches negative infinity as x approaches negative infinity. The domain is (0, +∞), and the range is (-∞, +∞).
To graph the given logarithmic function f(x), we can use the information provided in the table. The table gives us various values of x and their corresponding values of f(x). We can plot these points on a graph and connect them to visualize the function.
The table shows the following points: (1, 125), (-3, 1/25), (-2, 1/5), (-1, -1), (0, 5), (1, 125), (2, 2125), and (3, 3).
When we graph these points, we observe that the function starts at (-3, 1/25) and approaches positive infinity as x approaches positive infinity. Similarly, as x approaches negative infinity, the function approaches negative infinity.
From the graph, we can determine the domain and range of the function:
Domain: The domain of a logarithmic function is all real numbers greater than 0. In this case, since the function is defined for x = 1/5 and x = 3, the domain can be expressed as x ∈ (0, +∞).
Range: The range of a logarithmic function is all real numbers. In this case, the function takes values ranging from negative infinity to positive infinity. Therefore, the range can be expressed as f(x) ∈ (-∞, +∞).
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A hawker bought boxes of tomatoes at R18 per box at the market. He sold all but 5 boxes which went bad, at R25 per box. If he made a profit of R155, how many boxes of tomatoes did he buy?
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
Let's denote the total number of boxes the hawker bought as "x".
The cost of each box is R18, so the total cost of buying "x" boxes is 18x.
He sold all but 5 boxes, so he sold (x - 5) boxes at R25 per box. The revenue from selling these boxes is 25 * (x - 5).
The profit is calculated by subtracting the cost from the revenue, so we have:
Profit = Revenue - Cost
155 = 25 * (x - 5) - 18x
Simplifying the equation:
155 = 25x - 125 - 18x
155 + 125 = 25x - 18x
280 = 7x
Dividing both sides by 7:
x = 280 / 7
x = 40
Therefore, the hawker bought 40 boxes of tomatoes.
25 shaded squares 13 used what percentage used
Answer:
52% used.
Step-by-step explanation:
13/25=52/100=52%
Need help asap please .
Answer: 2011 and 2012
Step-by-step explanation:
f(x)= [tex]\frac{5x-5}{x^{2} -7x+6}[/tex]
Answer:
f(x)=5/(x-6)
Step-by-step explanation:
f(x)=(5x-5)/(x^2-7x+6)
f(x)=[5(x-1)]/[(x-1)(x-6)]
f(x)=5/(x-6)
The function V(r)=¹ can be used to find the volume of air inside a basketball given its radius. What does V(r)
represent?
the radius of the basketball when the volume is V
the volume of the basketball when the radius is r
the volume of the basketball when the radius is V
the radius of the basketball when the volume is r
OOO
Answer:
In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.
Step-by-step explanation:
The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."
The following is a list of shoe sizes for a group of 13 people.
4.5, 9.5, 8, 6.5, 10, 7, 8.5, 6, 7.5, 9, 6, 7, 11
Which of the following box plots best represents the numerical data?
A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 11.25 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.25. The lines outside the box end at 4.5 and 10. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 13 with tick marks every one-half unit. The box extends from 6.5 to 9 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 12. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 12.5 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 10.5. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
The box plot that best represents the numerical data is: A. A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
How to complete the five number summary of a data set?In order to determine the five-number summary for the survey, we would arrange the data set in an ascending order:
4.5,6,6,6.5,7,7,7.5,8,8.5,9,9.5,10,11
Based on the information provided about the list of shoe sizes for a group of 13 people, we would use a graphical method (box plot) to determine the five-number summary for the given data set as follows:
Minimum (Min) = 4.5.
First quartile (Q₁) = 6.25.
Median (Med) = 7.5.
Third quartile (Q₃) = 9.25.
Maximum (Max) = 11.
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Cuantos metros recorre un motociclista que va a 50Km/h en 3 horas
Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
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Here are ten numbers:
3 7 2 4 7 5 7 18 8
a) Write down the mode.
b) Work out the median.
c) Calculate the mean.
d) What is the range?
Step-by-step explanation:
a) The mode is 7, because it appears three times, which is more than any other number in the list.
b) To find the median, we need to arrange the numbers in order from smallest to largest:
2 3 4 5 7 7 7 8 18
The median is the middle number, which in this case is 7, since there are an equal number of values on either side of it.
c) To calculate the mean, we add up all the numbers and then divide by the total number of values:
(3 + 7 + 2 + 4 + 7 + 5 + 7 + 18 + 8) / 9 = 61 / 9 ≈ 6.78
So the mean is approximately 6.78.
d) The range is the difference between the largest and smallest numbers in the list:
18 - 2 = 16
So the range is 16.
Answer:
The numbers are 9 in total
Step-by-step explanation:
a) Mode 7
7 is the most occuring number.
b) Rearrange the numbers to find median
2, 3, 4, 5, 7, 7, 7, 8, 18
median=7
middle number is the median
c) Mean=2+3+4+5+7+7+7+8+18/9
mean=6.7
d) Range= Highest number - lowest number
18-2=16
I hope this helps a lot!
which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answer:
The slope of the graphed line is A. -5
Step-by-step explanation:
Since when we move one step in x direction, we move 5 steps downwards in y direction, so, the slope is,
m = y/x
m = -5/1
m = -5
Evaluate leaving your answer in a standard form 0.0048*0.81 /0.027*0.04
Step-by-step explanation:
When we simplify the expression, we get:
0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)
Using a calculator to evaluate the two fractions separately, we get:
0.0048 / 0.027 ≈ 0.1778
0.81 / 0.04 = 20.25
Substituting these values back into the original expression, we get:
(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25
Multiplying these two values together, we get:
0.1778 * 20.25 ≈ 3.59715
To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:
3.59715 ≈ 3.59715 × 10^(-3)
Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).
(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the better bank?
Answer:
(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the bet
(a) Compound interest is the interest earned on both the initial principal amount and any accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest that has been added to the principal over time.
(b) To calculate the amount Sumita will get at 10% simple interest when she deposits Rs. 21,000 in bank N for 3 years, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
In this case:
Principal (P) = Rs. 21,000
Rate of interest (R) = 10%
Time (T) = 3 years
Simple Interest = (21,000 * 10 * 3) / 100
Simple Interest = 6,300
Amount = Principal + Simple Interest
Amount = 21,000 + 6,300
Amount = Rs. 27,300
Therefore, Sumita will get Rs. 27,300 at 10% simple interest when she deposits it in bank N.
(c) To calculate the amount Sumita will get at 9% interest compounded annually when she deposits Rs. 21,000 in bank M for 3 years, we can use the formula for compound interest:
Compound Interest = Principal * [(1 + Rate/100) ^ Time] - Principal
In this case:
Principal (P) = Rs. 21,000
Rate of interest (R) = 9%
Time (T) = 3 years
Compound Interest = 21,000 * [(1 + 9/100) ^ 3] - 21,000
Calculating the compound interest:
Compound Interest = 21,000 * (1.09^3) - 21,000
Compound Interest ≈ 21,000 * 1.29503 - 21,000
Compound Interest ≈ 27,139.63 - 21,000
Compound Interest ≈ Rs. 6,139.63
Amount = Principal + Compound Interest
Amount = 21,000 + 6,139.63
Amount ≈ Rs. 27,139.63
Therefore, Sumita will get approximately Rs. 27,139.63 at 9% interest compounded annually when she deposits it in bank M.
(d) To determine which bank is better to deposit the sum, we compare the amounts received in bank N (simple interest) and bank M (compound interest).
In bank N, Sumita will receive Rs. 27,300, while in bank M, she will receive approximately Rs. 27,139.63.
Comparing the amounts, we can see that Sumita will get a slightly higher amount in bank N.
(e) The amount she will get from the better bank (bank N) is Rs. 27,300 - Rs. 27,139.63 = Rs. 160.37 more than bank M.
Step-by-step explanation:
hope it help
please answer ASAP I will brainlist
(a) The average cost in 2010 is $2088.82.
(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.
(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.4lnx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2010 - 2006) + 6
x = 4 + 6
x = 10 years.
Next, we would substitute 10 for x in the function:
g(10) = -1736.7 + 1661.4ln(10)
g(10) = $2088.82
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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HELP I WILL MARK BRAINLIEST AND GIVE 30 POINTS
The circle below is centered at the origin and has radius of 8. what is the equation ?
Step-by-step explanation:
h,k center is 0,0 and radius is 8
(x-0)^2 + ( y-0)^2 = 8^2
x^2 + y^2 = 64
IM NOT SURE, DO YOU WANT ME TO WORK IT OUT FOR YOU?
The height h(x), of an object is given by the function h(x) = -16x + 176x + 65
where x is time in seconds and h(x) is height in feet. When does the object reach its maximum height? Round your answer to two decimal places.
To find an object's maximum height, we need to find the vertex of this quadratic equation.
Answer: 5.50 seconds
Terms to know:
Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.
Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).
Step-by-step explanation:
The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]
Since we only are looking at the time it takes to reach maximum height we will only look at the x value.
[tex]x= \frac{-176}{2(-16)}[/tex]
[tex]x= 5.50[/tex]
What type of association does the following scatter plot represent?
Graph shows 0 to 10 on x and y axes at increments of 1. Dots are made at the ordered pairs 0, 10 and 1, 9 and 2,8 and 3,7 and 4,6 and 5,5 and 6,4.5 and 7,4 and 8,3.8 and 9,3.8 and 10,3.8
Positive linear association
Negative linear association
Positive nonlinear association
Negative nonlinear association
The data points form a straight line, suggesting a negative linear association.
Based on the given scatter plot, the association can be described as a negative linear association. A linear association refers to a relationship between two variables where the data points tend to cluster around a straight line. In this case, as the x-values increase, the corresponding y-values consistently decrease.
The scatter plot displays a clear negative slope, indicating that as the x-values increase, the y-values decrease in a linear fashion. This pattern suggests an inverse relationship between the two variables: as one variable increases, the other decreases proportionally.
The dots are arranged in a downward trend, with a clear linear pattern. This is characteristic of a negative linear association. The relationship between the variables can be described by a negative slope or a negative correlation coefficient.
It's worth noting that the scatter plot does not exhibit any curvature or nonlinear patterns. If there were a curvature present, indicating a non-linear relationship, it could be further classified as either positive or negative based on the direction of the curve.
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An author is writing and illustrating a new book. The gale diagram represent the ratio of area. In cm2 with text to area with illustrations .based on the ratio there 500cm2 of illustrations
Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10 x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y=2x+1
x012
Y
y = 10-x
x012
Y
= 10 - x.
y =
Y
10
-3 -2 -1
098
7
6
659
-5
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By completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
(a) To plot the lines y = 2x + 1 and y = 10 - x, we need to complete the tables of values and then plot the points on the axes.
For the line y = 2x + 1, we can choose some values of x and calculate the corresponding y values:
x | y
0 | 1
1 | 3
2 | 5
For the line y = 10 - x, we can also choose some values of x and calculate the corresponding y values:
x | y
0 | 10
1 | 9
2 | 8
Plot the points (0, 1), (1, 3), and (2, 5) for the line y = 2x + 1, and the points (0, 10), (1, 9), and (2, 8) for the line y = 10 - x on the provided axes.
(b) To find the solution to the simultaneous equations y = 2x + 1 and y = 10 - x,
we need to identify the point(s) where the two lines intersect on the graph.
From the plotted lines, we can see that they intersect at the point (3, 7). Therefore, the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7.
In conclusion, by completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
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Ahmed has five more CDs than one-half the number of CDs Julia has. In this situation, what does One-halfc+ 5 represent?
the number of CDs Ahmed has
the number of CDs Julia has
the number of CDs Ahmed has more than Julia
the number of CDs Ahmed and Julia have altogether
The number of CDs Ahmed has: The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct. Option A
According to the given information, Ahmed has five more CDs than one-half the number of CDs Julia has. One-half of the number of CDs Julia has can be represented as (1/2) * c. Ahmed has five more CDs than this value, so we can express the number of CDs Ahmed has as:
Ahmed's CDs = (1/2) * c + 5
Now, let's analyze the options provided:
A. The number of CDs Ahmed has:
The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct.
B. The number of CDs Julia has:
The expression (1/2) * c + 5 does not directly represent the number of CDs Julia has. It represents the number of CDs Ahmed has. Therefore, this option is incorrect.
C. The number of CDs Ahmed has more than Julia:
This option is incorrect because the expression (1/2) * c + 5 represents the absolute number of CDs Ahmed has, not the difference between the number of CDs Ahmed and Julia have.
D. The number of CDs Ahmed and Julia have altogether:
The expression (1/2) * c + 5 represents only the number of CDs Ahmed has. It does not include Julia's CDs. Therefore, this option is incorrect.
In conclusion, the expression (1/2) * c + 5 represents the number of CDs Ahmed has.
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The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
6
75
80
85
90
95
3
9
5
7
8
2