Answer:
⟶ We can express the sum 1^2 + 2^2 + 3^2 + ... + 750^2 using summation notation as:
∑i^2, where i goes from 1 to 750.
⟶ Here, the symbol ∑ represents the summation, and i is the index variable, which takes on the values 1, 2, 3, ..., 750. The expression i^2 is the term being summed.
⟶ So the sum can be written as:
∑i^2 = 1^2 + 2^2 + 3^2 + ... + 750^2
⟶ Note that the upper limit of the index variable is 750, which corresponds to the last term in the sum.
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Answer:
[tex]\sum \limits^{750}_{n=1} {n^2}[/tex]
Step-by-step explanation:
General explanation of summation notation
Any sum of terms whose format is the same can be represented more concisely using a Summation symbol.
The Summation symbol is a capital greek letter Sigma: [tex]\sum[/tex]
The summation will take a general format of each term, and increase a "dummy variable" by 1, summing together terms until the summation is complete. To write the summation expression, find the common format of each term, and write it using a "dummy variable" to represent the number that is changing.
If the change of the number within each term increases by 1 each time, that makes the transition easier because the dummy variable increases by 1. If the change of the number within each term does not change by 1 each time, using summation notation can be more challenging, as one needs to develop a formula to represent the amount that it is changing each time.
The common format of each term & the changing number
In our case, each term is some number squared, and the number that is squared changes from 1, to 2, to 3, ... and so on .. up to 750 (changing by 1 each time). Since the number that is square changes by 1 each time, that will be our "dummy variable".
Using "n" for the "dummy variable", our terms look like [tex]n^2[/tex]
The start and end of the list
Lastly, to specify where the list starts and ends, we write where the list starts (lowest number) at the bottom with the "dummy variable", and where the list ends (largest number) at the top.
So, in the end, the summation would look like this: [tex]\sum \limits^{750}_{n=1} {n^2}[/tex]
This represents adding a bunch of terms that look like [tex]n^2[/tex], starting at n=1, each time, increasing the value of n by 1, and stopping with the last term when n=750.
Extension of knowledge (NOT about THIS problem)
For a similar example where the changing number doesn't increase by 1 each time, look at a similar sequence of, where it's just the odd numbers squared up to 99:
1^2 + 3^2 + 5^2 + … + 99^2
While the terms do have the format of a number squared, since the number that is squared isn't just increasing by 1 each time, there would need to be a formula to describe how they are increasing. One way to represent that would be:
[tex]\sum \limits^{50}_{n=1} {(2n-1)^2}[/tex]
Note that this does cause the final endpoint of the dummy variable to not necessarily be intuitive, but the "99 squared" is the 50th term (observe 2*50-1 is 99).
Angle A and B are complementary angles and angle B and C are supplementary angles. If angle A equals 20 what is the measure of angle C?
Answer:
Angle B measures 70°, so angle C measures 110°.
20° + B = 90°, so B = 70°.
70° + C = 180°, so C = 110°.
Using the graphing method, which of the following choices is the solution of the system: y = -x − 4 4y − 2x = 8 (-6, -2) (-4, 0) There are infinite solutions. There are no solutions.
The solution of the system of equations is the point (-4, 0)
How to solve the system of equations?Here we have the system of equations:
y = -x - 4
4y - 2x = 8
To find the solutions graphically, what we need to do is graph both equations on the same coordinate axis, and then find the points where the graphs of the equations intercept. These points are the solutions of the system.
On the image at the end, you can see the graph of the system of equations, there we can see that the lines intercept at the point (-4, 0), so that is the solution.
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3. In the right triangle below, what is the measure of RST?
A 10°
B. 30°
C. 60°
D. 90°
The measure of angle RST is 90°.
option D.
What is the measure of RST?The measure of angle RST is calculated by applying the principle of a right angle triangle as shown below;
A right-angled triangle, also known as a right triangle, is a triangle in which one of the angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are known as the legs.
From the given diagram, the measure of angle RST is calculated as follows;
∠S = 90 (since this angle has a symbol of right angle)
So the other two angles, R and T are complementary.
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Plot and connect the points A(4, 6), B(4, 0), C(1, -3), and D(1, 3), and find the area of the parallelogram formed.
Answer:
18 square units
Step-by-step explanation:
The parallelogram has been plotted in the attached figure
The area of a parallelogram is b x h
where b is one side and h is the vertical distance between the two bases
In the figure, we see that base = AB is parallel to the y-axis
This means the y-coordinates of A and B are the same and the distance is obtained by taking the absolute difference between the x-coordinates of A and B
b = |x1 - 2| = |6 - 0| = 6
The height h is a perpendicular line from point D(1, 3) to the base which touches the base at point E
Since this line is horizontal to the x-axis in the figure, the y coordinates of the endpoints of the line are the same i.e y1 =3 and y2 = 3
Therefore h = absolute difference between the x coordinates
= |1-4| = 3
Given b = 6, h = 3
area = 6x 3 = 18 square units
Enter your answer in the box.
Answer:
I think it may be 160?
Step-by-step explanation:
400/5 is 80 there's 2 yellow so 2x80= 160 times
(22-26)²+(34-26)²+(30-26)²+(14-26)²+(30-26)[tex]\frac{x}{y}[/tex]5
Answer:
[tex]20x+240y/y[/tex]
Step-by-step explanation:
1. Subtract the numbers
2. Evaluate the exponents
3. Subtract the numbers, again
4. Have a great day and thx for your inquiry :)
Jen’s soccer team is playing 4 games next week. How many different outcomes are there for the four games
Answer:
4 outcomes
Step-by-step explanation:
16 Bob is at a Carnival and will spin each spinner one time.
AB
4
1966
3
5
2
6 1
16
2
5
What is the probability that the spinner on the left will land on a 6 and the
spinner on the right will land on a shaded area?
3
4
213112
17 The equation 3x + 4 = 16 is modeled below:
The probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.
Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.
The probability that the spinner on the left will land on a 6 is calculated as,
P₁ = 2 / 12
The spinner on the right will land in a shaded area is,
P₂ = 8 / 12
The total probability will be,
P = ( 2 / 12 ) x ( 8 / 12 )
P = 1 / 9
Therefore, the probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.
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Help please (elementary stats)
The average weight of a sample of objects is 94.83 pounds and the spread of the weights around the mean is measured by the sample standard deviation, which is 31.16 pounds.
The given data shows the weights (in pounds) of adult wild mountain lions captured and released for the first time in the San Andres Mountains.
(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean weight x and sample standard deviation s.
[tex]x = (70 + 107 + 130 + 128 + 60 + 64) / 6 = 94.83 \pounds\\\\s = \sqrt{\frac{(70 - 94.83)^2 + (107 - 94.83)^2 + ... + (64 - 94.83)^2} {5}}[/tex]
= 31.16 pounds
Therefore, the sample mean weight x is 94.83 pounds and the sample standard deviation s is 31.16 pounds.
(b) To find a 75% confidence interval for the population average weight u of all adult mountain lions in the specified region, we can use the formula:
CI = x ± t*(s/√n)
where CI is the confidence interval, x is the sample mean weight, t is the t-score for the desired confidence level (75% in this case), s is the sample standard deviation, and n is the sample size (6 in this case).
From the t-table, the t-score for a 75% confidence level with 5 degrees of freedom is 2.015.
Plugging in the values, we get:
CI = 94.83 ± 2.015*(31.16/√6) = (63.6 pounds, 126.1 pounds)
Therefore, we can be 75% confident that the true population average weight of all adult mountain lions in the specified region is between 63.6 pounds and 126.1 pounds.
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The graph of which equation passes through the point
(4, - 3) and has a slope 4
A.5x+4y=8
B.5x - 4y = 8
C.4x + 5y = 8
D.4x - 5y = 8
The equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.
To determine which equation passes through the point (4, -3) and has a slope of 4, we can substitute the values of x and y into each equation and check if the resulting equation is true.
Let's substitute x = 4 and y = -3 into each equation:
A. 5x + 4y = 8
Substituting x = 4 and y = -3:
5(4) + 4(-3) = 20 - 12 = 8
The equation is true for points (4, -3).
B. 5x - 4y = 8
Substituting x = 4 and y = -3:
5(4) - 4(-3) = 20 + 12 = 32
The equation is not true for points (4, -3).
C. 4x + 5y = 8
Substituting x = 4 and y = -3:
4(4) + 5(-3) = 16 - 15 = 1
The equation is not true for points (4, -3).
D. 4x - 5y = 8
Substituting x = 4 and y = -3:
4(4) - 5(-3) = 16 + 15 = 31
The equation is not true for points (4, -3).
Therefore, the equation that passes through the point (4, -3) and has a slope of 4 is option A: 5x + 4y = 8.
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A company studied how much they pay employees. They found the mean and median annual salaries. These values are given in the table.
Annual Salary Data
Mean Annual Salary $62,000
Median Annual Salary $35,000
Which measure of center is best to describe salaries at the company? Select the statement that BEST explains your choice.
a. the mean, because people who earn too little make the median too small
b. the mean, because most workers earn a salary that is near this value
c. the median, because it is the measure of center with the lower value
d. The median, because people who earn a lot make the mean too large
The best measure of center to describe salaries at the company is the median. The Option D is correct.
Why is median best measure to describe salaries?The reason is that the median is less affected by extreme values or outliers which can greatly affect the mean. In this case, the mean annual salary is $62,000 while the median is only $35,000.
This large difference suggests that there are some very high earners at the company that are pulling up the mean. The median indicates that half of the employees earn less than $35,000 and half earn more which gives a more accurate picture of the typical salary at the company.
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can someone explain how five is the correct answer.
The number of unique preference orders that are represented in the table would be B. Five.
How to find the number of unique preference orders ?An individualized preference order is one way to assign a hierarchal ranking to an assortment of options. This ordering is recognized as "unique" because each item is assigned its own rank, with no two elements sharing the same level of priority.
From what is shown on the table, we have Voters 2, 4, 5 and 7 having a unique order. From these four voters, we therefore have four unique preference orders.
However, there is another unique preference order which is the shared preference order of Voters 1. 3 and 6 because this is unique preference order shared by three people.
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when given angle measures of 25,65,and 90,is it possible to draw a triangle,possible to draw only one triangle,or possible to draw more than one triangle?explain.
The total angle measurement of a triangle sum above is 180°. So yes, it is possible to only make a right angle triangle but impossible to draw a triangle
What is the triangle?To check if a triangle can be drawn with 25°, 65°, and 90° angles, we use the Triangle Angle Sum Theorem stating that all triangle angles add up to 180 degrees.
If you add all the angles together (25 + 65 + 90 = 180°), We can draw a triangle based on this sum, but we only consider the angles' nature. The triangle has angles of 25°, 65°, and 90°, making it a right triangle. It only applies to right triangle and not others triangle .
Note that based on the given angle measures of 25°, 65°, and 90°, it is impossible to draw a triangle as it does not follow the triangle inequality property.
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Factor completely. 2x^2 − 7x − 4
Answer:
(2x + 1) (x - 4)
Step-by-step explanation:
2x² - 7x - 4.
need two number that add up to -7, but that multiply together to get -4.
(2x + 1) (x - 4) = 2x² - 4(2x) + x - 4 = 2x² - 8x + x - 4 = 2x² - 7x - 4
8 1/2 x 4 1/4 = Answer
Answer:
Answer is 36 1/8
Step-by-step explanation:
8x4 is 36. 1/2 x 1/4 is 1/8
Answer:
36 1/8
Step-by-step explanation:
8 1/2 = 17/2 x 17/4 = 289/8 = 36.125 = 36 1/8
the ratio of 2/3 to 8 as a fraction in simplest form
To write the ratio of 2/3 to 8 as a fraction in simplest form, we need to divide the numerator and denominator by their greatest common factor (GCF).The GCF of 2 and 8 is 2.So, we divide both the numerator and denominator by 2:2/3 ÷ 8/1 = (2/3) ÷ (8/1) = 2/3 x 1/8 = (2 x 1) / (3 x 8) = 2/24Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor again.The GCF of 2 and 24 is 2.So, we divide both the numerator and denominator by 2:2/24 ÷ 2/2 = (2/24) ÷ (2/2) = 2/24 x 1/2 = (2 x 1) / (24 x 2) = 1/12Therefore, the ratio of 2/3 to 8 as a fraction in simplest form is 1/12.
Answer:
How to find Ratio?
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10
In order to find the ratio of a certain number to another number or the relation of each other, we also need to know the concept of fraction and percentage.
1/12 or 1 to 12
The ratio is 2/3*8=23⋅8=2/24=1/12
So it is 1 to 12
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A car left Town A at 9:30 a.m. and reached Town B at 11:30 a.m. Its average speed was 60 km/h. Find the distance between Town A and Town B.
Answer:
120 km
Step-by-step explanation:
its average speed was 60 km an hour and it took 2 hours from town a to town b so 60km + 60km = 120
[tex]{\large {\orange{\underline {\underline {\mathcal {♡AnSwER♡⤵}}}}}}[/tex]
Left Town A at 9:30 am
Reached town B at 11:30 a.m
Therefore, Time taken by the car is =( 11:30 - 9:30) hrs =2 hrs
The speed of the car =60 km/h
So, the distance between Town A and B is = (Speed × Time) =( 60 × 2 )km =120 km.
The distance between Town A and B is 120 km. (Ans)
Hope it helps you
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank ~you~:)}[/tex]
A car dealership has 10 cars on display. They have 7 cars and 3 trucks. What decimal number shows the number of trucks they have on display?
Question
Which of the following is equivalent to 12x + 8?
○ 4(3x + 2)
O4(3x + 8)
O4(3x + 2x)
O 20x
Answer:
the first one
Step-by-step explanation:
reason - 4 times 3 is 12 and 4 times 2 is 8 so 12x+8
caculate the circumference of a circle whose diameter is 28cm.
Answer: about 87.96459430051421
Step-by-step explanation: 28 x 3.14 = the answer
You roll a dice. Find the following probabilities. Round to the nearest hundredth if necessary.
Event
Work
17. The the probability of rolling a 3 or a
number less than 4.
18. The probability of rolling a number less
than five or an odd number.
19. The probability of rolling a four or an
odd number
Answer
Answer:
18. The probability of rolling a number less than five or an odd number
Hope this helps! :)
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FIND THE TOTAL SURFACE AREA
30 Length
12 base
9 Hieght
The surface area of the rectangular prism is 1476 square units
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
30 mm by 12 mm by 9 mm
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)
Evaluate
Area = 1476
Hence, the area is 1476 square units
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when do you think pressure can be negative
Answer:
Yes it can be negative
Step-by-step explanation:
For example, in a vacuum, there is no atmospheric pressure and the pressure is zero. If we introduce a sealed container into the vacuum and pump out the air, the pressure inside the container will be negative compared to the pressure outside the container.
What are the coordinates of S? the image is below
The coordinates of point S are (4, 3.5)
How to find the coordinates of point S?Remember that the coordinates of a point are written in the notation (x, y), such that the first value is the value in the horizontal axis, and the second value is the value in the vertical axis.
Each one of the squares is one unit, then the x-value of the point S is:
x = 4
And for the y-value we can see that the point is halfway between the third and the fourt lines, then:
y = 3.5
Thus, the coordinates of point S are (4, 3.5)
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PLEASE HELP
Angle RST is its own complement. What is the
measure of the angle that is supplementary to angle RST?
the measure of the angle that is supplementary to angle RST is 90 degrees
How to determine the angleTo determine the value of the angle, we need to know the following;
Complementary angles are defined as a pair of angles whose sum is equal to 90 degreesThese angles are mostly right -anglesSupplementary angles are defined as a pair of angles whose sum is equal to 180 degreesthese angles are mostly on a straight lineFrom the information given, we have that;
Angle RST is its own complement
Then, angle RST =90 degrees
The supplementary angle should be y
Then,
RST + y= 180
substitute the values
y = 180 - 90
subtract the values
y= 90 degrees
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The area of a rectangle painting is 3339cm^2. If the length of the painting is 63 centimeters, what is its width?
Answer:
Step-by-step explanation:
Width = Area / Length
Width = 3339 cm^2 / 63 cm
Width = (1113/21) cm
Width = (371/7) cm
Width = 52 cm
Use six pairs of the corresponding parts to explain why these triangles are similar
The corresponding angles and sides that show that the triangles are similar are: <A ≅ <R; <K ≅ <T; <M ≅ <L
RL/AM = RT/AK = TL/KM = 1.5.
What are Similar Triangles?Similar triangles are triangles that look alike but might be bigger or smaller than each other. This means that their matching or corresponding angles are the same and their matching sides have the same proportional length.
Therefore, from the image, we have corresponding pairs of angles that are congruent as follows:
Angles A and R
Angles K and T
Angles M and L
The corresponding sides that are proportional are:
AM and RL, which is RL/AM = 6/4 = 1.5
AK and RT, which is RT/AK = 7.5/5 = 1.5
KM and TL, which is TL/KM = 9/6 = 1.5
Therefore, the triangles are similar.
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Which expression is equivalent to..?
The equivalent expression is the one in the last option:
[tex]\sqrt[10]{y}[/tex]
Which expression is equivalent to the given one?Here we want to find an expression equivalent to:
[tex](\frac{1}{\sqrt{y} } )^{-1/5}[/tex]
Remember the two rules for exponents that we need to use here:
[tex]x^{-n} = (1/x)^n[/tex]
[tex]x^{1/n} = \sqrt[n]{x}[/tex]
Using the first rule, we can rewrite our expression as:
[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5}[/tex]
Now we can rewrite the root of a root to get:
[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5} = \sqrt[5]{\sqrt{y} } = \sqrt[10]{y}[/tex]
Where in the last step we just multiplied the exponents for the roots, we can see that the correct option is the last one.
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Which is equivalent to (4 + 44)?
Answer:
48
Step-by-step explanation:
just add the numbers. 48 is equal to (4+44)
have a great day and thx for your inquiry :)
Construct a stem-leaf Plot (Final arrangement): 18, 17, 23, 28, 13, 14, 15, 27, 21, 18, 12, 15, 41, 22, 14, 19, 18, 22, 33, 16
Stem-leaf plot for the given data:
1 | 2 3 4 5
2 | 1 2 2
3 | 3 3
4 | 1
The stem represents the tens digit and the leaf represents the ones digit of the data points. For example, the number 18 is represented as 1|8 in the plot.
A stem-and-leaf plot for the given data:
1 | 2 3 4
---+-------
1 | 2 2
2 | 2 2 3 8
3 | 3 3
4 | 1
5 |
6 | 6
7 | 7
8 |
In this plot, the tens digit is used as the stem, and the ones digit is used as the leaf. For example, the first two numbers in the data set are 18 and 17, which have stems of 1 and leaves of 8 and 7, respectively. These are shown in the first row of the plot as "1 | 8 7". Similarly, the number 23 has a stem of 2 and a leaf of 3, so it is shown in the second row as "2 | 3". The remaining numbers are arranged in the same way.
The numbers are arranged in ascending order within each row, and there are blank spaces for stems that do not appear in the data.
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