Ques) What is the symbol (∑)?
This symbol is used to denote the sum of multiple numbers.
This symbol is generally put by an index that varies to encompass all terms that must be considered in the sum of all the numbers.
In order to calculate the arithmetic mean of a set of data, the first step is to add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean
Mean = ∑ x/n
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A candidate for office claims that "there is a correlation between television watching and crime."
Criticize this statement on statistical grounds.
The correct option regarding the statement is given as follows:
A. There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.
What are qualitative and quantitative variables?The variables are classified as qualitative or quantitative as follows:
Qualitative variables assume labels as values.Quantitative variables assume numbers as values.The relevance of the variables according to association and correlation are given as follows:
Qualitative variables can have association.Quantitative variables can have correlation.The variables in this problem are given as follows:
Television watching -> yes/no -> qualitative.Crimes committed -> yes/no -> qualitative.As they are qualitative variables, they can have association, and thus option A is correct.
Missing InformationThe options are given by the image presented at the end of the answer.
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Out of a group of 360 students, exactly 18 are on the track team. What percent of the students are on the track team?
if we take 360 to be the 100%, what's 18 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 360 & 100\\ 18& x \end{array} \implies \cfrac{360}{18}~~=~~\cfrac{100}{x}\implies 20=\cfrac{100}{x} \\\\\\ 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
what algebraic expression represents a number increased by 5
Answer: x+5
Step-by-step explanation:
Because we don't have a number so we call it x. And to increase by 5 just need to +5. So x+5
ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
Which trigonometric functions have the same maximum value? y = arcsinx and y = arccosx y = arcsinx and y = arctanx y = arctanx and y = arcsecx y = arccosx and y = arcsecx.
Trigonometric functions have the same maximum value y = arcsinx and y = arccosx.
What is Trigonometric Function?
Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. It implies that these trig functions provide the relationship between a triangle's angles and sides.
Arcsin, Arccos, Arcsec, and similar symbols are used to represent inverse trigonometric functions.
Inverse functions refer to the trigonometric operations that are used to determine an angle from any of the angle's trigonometric ratios.
When solving inverse trigonometric equations, the following formula is used:
Arcsinx = Arcsinx -
arccosx = pi-arccosx.
Arctan = Arctan - Arctan
arsecx = pi - arsecx
The maximum values we obtain from the following equations are:
arcsinx = -1 to 1
arccosx = -1 to 1
arctanx = -pi/2 to pi/2
arcsecx = ∞
So the trigonometric functions which have the same maximum value is arcsinx and arccosx.
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Which of the following are essential elements of hypothesis testing?
-It uses probability theory to determine if a hypothesis is a reasonable statement.
-It makes use of sample data.
The following are crucial factors in hypothesis testing:
It employs probability theory to evaluate if a hypothesis is a valid claim.It employs sample data.Explain the term hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.
The type of data being used and purpose of the study will determine the methodology the analyst uses. A basic hypothesis can anticipate a causal relationship between variables, i.e., that one has an impact on the other. This is known as hypothesis testing, and it uses sample data to determine the plausibility of a hypothesis.It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an investigation are reliable.Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.
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A drawing ha a cale of 1:30. An a drawing, a kitchen i a rectangle meauring 12cm by 27cm. A bedroom ha an actual area of 300000cm
which ha the bigger actual area, the kitchen or the bedroom?
you mut how your working
Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.
As per the given question,
Given drawing scale is:
1 : 30
Shape of the kitchen is rectangle with measurements = 12cm by 27cm
Using scale :
Length = 12cm
Actual length = 12 × 30
= 360cm
Width = 27cm
Actual width = 27 × 30
= 810 cm
Actual area of kitchen = 360 × 810
= 291,600 cm²
Actual area of bedroom = 300,000cm²
300,000 > 291,600
Actual area of bedroom > Actual area of kitchen
Therefore, actual area of bedroom is bigger than the actual area pf kitchen.
The complete question is:
A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
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Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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Suppose a designer has a palette of 15 colors to work with, and wants to design a flag with 5 vertical stripes, all of different colors.
How many possible flags can be created?
The number of flags that could possibly be created, given the palette of colors to work with, and the number of stripes, is 360, 360 flags.
How to find the number of flags?The designer has the choice to pick from 15 colors to work with. They will then pick another color, and then another, until they pick five colors to make stripes.
When they pick a single color, the number of choices drops to 14 colors. When they pick 5 colors, they will be left with 11 colors.
The number of possible flags is therefore:
= 15 x 14 x 13 x 12 x 11
= 360, 360 possible flags
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Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
For every point on the graph of F(x), there is a point on the graph of F1(x)
with exactly the same coordinates.
A. True
B. False
Dilate rectangle ABCD by
a scale factor of ½ using E
as the center.
As we dilate rectangle ABCD by a scale factor of 1/2 and use E as the center, the coordinates of the point D' = (2, -1).
What is meant by rectangle?A rectangle is a quadrilateral in Euclidean plane geometry with four right angles.
The coordinates of the rectangle's points A'B'C'D' are as follows:
A' = the point's coordinates (-2, -1)
B' = the coordinates of the point (-2, 1)
C' = the coordinates of the point (2, 1)
D' = the coordinates of the point (2, -1)
Using the point P as the chart's origin, we get;
The coordinates of point B are (-4, 2), and the coordinates of point C are (4, 2).
Given that the sides are parallel to each other, the coordinates of point A = (-4, -2) The coordinates of point D = (4, -2)
We have; given that the sides are parallel to the axis.
The segment length AB = 2 - (-2) = 4
The segment length BC = 4 - (-4) = 8
The segment length CD = 2 - (-2) = 4
The segment length AD = 4 - (-4) = 8
As a result, a 1/2 dilation yields;
The segment length A'B' = AB/2 = 4/2 = 2
The segment length B'C' = BC/2 = 8/2 = 4
The segment length C'D' = CD/2 = 4/2 = 2
The segment length A'D' = AD/2 = 8/2 = 4
Point A' coordinates = Point A/2 coordinates = (-4, -2)/2 = (-2, -1)
= (-4, 2)/2 = (-2, 1) (-2, 1)
The coordinates of the point B' = (-2, 1) The coordinates of the point C' = (4, 2)/2 = (2, 1)
C' = the coordinates of the point (2, 1)
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What is the slope that passes through (1,2) and (2,6)
Answer:
4
Step-by-step explanation:
use slope formula y2-y1/x2-x1
6-2/2-1
4/1
4 is the slope
Hopes this helps please mark brainliest
Solve the system. Explain your answer using words, symbols, or both. please show your work thank you.
x+3y=8
x+y=2
The value of x and y is 3
What is meant by mathematical equation ?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
Let the equations be
x + 3y = 8 ..............(1)
x + y = 2 ..............(2)
substracting equation 1 from 2
(x + 3y) - (x + y ) = 8 - 2
x + 3y - x + y = 6
3y - y = 6
2y =6
y = 6/2
y = 3
multiply the equation 2 with value of 3
x + y=2*3
x+y =6
x+3 = 6
x = 6 - 3
x = 3
Therefore the value of x and y is both are 3
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a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Helppppp, I don’t know what to do, I just really need the answer
The completed statement on the exponential model that fits the data in the question is presented as follows;
The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.
What is a correlation coefficient?The correlation coefficient is an indication of the level at which the variables are interdependent.
The table of values in the question can be entered into a spreadsheet application as follows;
In the spreadsheet application, enter Year since 1960 values in a column, and the Plastic Production in an adjacent columnSelect the all the data entered into the spreadsheet document such as MS Excel, then select the Insert tabIn the charts section select scatter plot to create a scatter plot of the dataIn the Design tab, that appears when the chart is selected, select the Add Chart Element button access the Trendline functionSelect the Exponential trendline from the menu for trendlinesThe exponential trendline is then created by the spreadsheet applicationThe equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)
The growth rate from the above exponential function is 7·88% per year
The production 15 years after 1960 is therefore;
f(15) = 9.2179·e^(0.0788 × 15) ≈30.06
The number of plastic produced 15 years after 1960 is about 30 million metric tons
The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model
The prediction is correct based on the strong correlation between the year and the number of plastic produced.
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Boden's account has a principal of $600 and a simple interest rate of 3.3%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &4 \end{cases} \\\\\\ A=600[1+(0.033)(4)] \implies A=600(1.132)\implies A = 679.2[/tex]
Answer: photo
Step-by-step explanation: picture
a photo has a width to length ratio of 2:3. if the width of the photo is 4.8 cm, the length of the photo is
The length of the photo having a width to length ratio of 2:3 is 6.9 cm.
What is length?Length is the distance between two points.
To calculate the length of the photo, use the formula below.
Formula:
L = W/R............ Equation 1Where:
L = Length of the photoR = Width to length ratio of the photoW = Width of the photo.From the question,
Given:
W = 4.6 mR = 2:3 = 2/3Substitute these values into equation 1
L = 4.6/(2/3)L = 4.6×3/2L = 6.9 cmHence, the length of the photo is 6.9 cm.
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T/F the proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the .
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.
What is coefficient of determination?
The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.
R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.
R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.
You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:
Dots represent the observations.
The line of best fit, or predictions of the model, is displayed as a black line.
Purple lines represent the deviations (the residuals) between the data and their expected values.
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What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b = ?
Answer:
3
Step-by-step explanation:
Find x and y values that make both y=−2/3x+3 and y=2x−5 true.
What is the ordered pair for your solution?
The ordered pair is (3, 1) which is the intersecting point of these two equations.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.
Now the solution to this system is the common intersecting point of these equations.
With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.
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to construct a confidence interval using matched pairs, we must compute the standard deviation of the
We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated.
The complete question is:
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?
The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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In 8 day, a ample of vanadium-48 decay to 1/√2 of it original amount. Determine the half-life of vanadium-48
The half-life of vanadium-48 is 16 days.
What is half life?
The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.
According to law of radio active decay, IN=N
N-- amount of sample present
N1--- initial amount of sample
Decay 0 constant
Half life = 16 days
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Examine the graph of the function.
What is the rate of change of the function?
The rate of change of the function is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the function are 3 and 5
The inputs of the function are 1 and 2.
We have,
We will find two points on the graph.
The points on the graph are:
(0, 5), (1, 3), and (2, 1)
We can choose any two points.
(0, 5) and (1, 3)
The rate of change of the function.
= (3 - 5) / (1 - 0)
= -2/1
= -2
Thus,
The rate of change of the function is -2.
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Pls helppppppppppppp quick
Answer: (0, -3)
Step-by-step explanation:
You start from the x axis which is zero and then u go to the y axis and look for -3
14. On the test, Zeke answered 85% of the
questions correctly. If there were 60 problems
on the test, how many did Zeke answer
correctly?
What is the equation of a vertical ellipse with a major axis = 14, a minor axis = 12,
and a center of (3,5) ?
The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.
How to determine the standard form of the equation of the ellipse
Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:
(x - h)² / a² + (y - k)² / b² = 1, b > a
Where:
(h, k) - Center of the ellipse.a, b - Length of the semiaxes.If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:
(x - 3)² / 12² + (y - 5)² / 14² = 1
(x - 3)² / 144 + (y - 5)² / 196 = 1
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One of the brightest stars in the sky is Sirius , which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. How far, in miles, is Sirius ?
If one of the brightest stars in the sky is Sirius , which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. The distance is 5.29 x 10^13 miles.
What is distance?Distance can be defined as the length of an object or how far an object is from another object.
Given data:
9 light years
5.88 x 10^12 miles
Now let find the how far, in miles, is Sirius
Distance = 5.88 x 10^ 12 miles× 9 light year
Distance = 52,920,000,000,000
Distance = 5.29 x 10^13 miles
Therefore we can conclude that the distance is 5.29 x 10^13 miles.
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