(b) The number of people to be selected from those who responded "yes" in the stratified random sample is 14.
(c) A statistical advantage of using the stratified random sample instead of the simple random sample is that it ensures a proportional representation of each stratum (in this case, "yes" and "no" responses) in the sample, reducing the risk of bias and increasing the accuracy of the results.
The calculation is determined by dividing the total number of samples (20) by the number of strata (2) plus 1, then multiplying by the number of samples for each stratum. The result of 20 / (2 + 1) * 2 is
20 / 3 * 2
= 40 / 3
= approximately 13.33, which is rounded up to 14 people.
In a simple random sample, the individuals selected may not accurately reflect the proportions of the two responses in the population. This can result in incorrect conclusions and decision-making. With the stratified random sample, the proportions of "yes" and "no" responses in the sample are maintained, providing a more accurate representation of the population.
Additionally, stratified random sampling allows for separate analysis of each stratum, which can provide additional insights into the population. Overall, stratified random sampling is a more robust method for obtaining accurate and representative results in a survey setting.
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Which point is a solution to the system of linear equations? y = −x + 2 x − 3y = 6
1,014 is the median value of the given population parameters. This value is the middle value. in the ordered list of data values. This value in a set of 11 will be the 1014 number in order. Therefore, years will have totals at or below the median.
Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.
How is the median value determined?When working with a tiny data collection, you must first count the number of data points (n) and organise them in ascending order. In the case of an unequal distribution of data points, the rank of the data point whose value is the median is determined by adding 1 to the total number of points and dividing the results by 2.In statistics, the median is the value that, when placed in order, falls in the centre of the supplied collection of data. Either descending or ascending order can be used to arrange the data or observations.Since 1014 is at median which tells us that 50% of the values are equal.1014 * 11 = 11014.
Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.
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i flip a coin three times and then another three times if the number of heads is the same the first and second time i win is this game worth playing
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. This is worth playing game.
Let's assume that player A wins if both sets of coins are fair and have an equal number of heads.
The likelihood of this = (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2
The likelihood of this = 1/64 + 9/64 + 9/64 + 1/64
The likelihood of this = (1 + 9 + 9 + 1)/64
The likelihood of this = 20/64
The likelihood of this = 5/16
If the two sets are different, let's say B triumphs.
The likelihood of this = 1 - 5/16 = 11/16
Therefore, if A wins 3 dollars and loses 1 dollar, then A's predicted net gain is
= 3 × 5/16 - 1 × 11/16
= 15/16 - 11/16
= (15 - 11)/16
= 4/16
So this game is defiantly worth playing game.
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The complete question is:
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?
geometry unit 7 : angles of polygons & parallelograms
find the value of x
Using the relationships between the angles of a parallelogram, the value of x is 12.55°.
Finding the value of x:A parallelogram has opposite angles that are equal, and adjacent angles that add up to 180°.
We can start with angles a and c. Since they are both equal to 90°, that means that angle b must also be 90°.
We can now use this information to find the value of x.
We can use the fact that angles a, b, and c add up to 270° to find x.
Since angles a and c are both 90°, that means that angle b must be 90°.
We can then solve for x by subtracting 190° (90° + 100°) from 270° and dividing by 7.
In order to solve for the value of x, we must use the properties of a parallelogram.
Since a parallelogram has four sides and four angles, the sum of the interior angles must equal 360°.
Therefore, we can set up an equation using the given angles and the unknown angle of x to solve for the value.
95° + (7x - 4)° + 90° + (3x + 23)° + (9x - 6)° = 360°
20x + 109° = 360°
20x = 251°
x=12.55°
Therefore, the value of x is 12.55°.
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select yes if the determinant shows that the matrix will reduce to an identity matrix; select no if it does not. [ 3 0 5 1 ]
No. The determinant doesn't show that the matrix will reduce to an identity matrix.
The determinant of a matrix is a scalar value that can be used to determine whether a matrix is invertible or not. If the determinant is non-zero, the matrix is invertible and can be reduced to an identity matrix through row operations. If the determinant is zero, the matrix is not invertible and cannot be reduced to an identity matrix.
In this case, the determinant of the matrix [3 0 5 1] is equal to 3 * 1 - 0 * 5 = 3, which is non-zero. Therefore, this matrix can be reduced to an identity matrix through row operations, but the determinant does not indicate this directly.
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b) The growth rate of covid patient is 5% per hour. If the number of covid patients in the morning 9am is 44,100, what was the number of patient 7am sharp?
Answer:
36,900
Step-by-step explanation:
it's right I just do not know how to explain lol
Which is the graph of g(x)?
3,
x < -2
g(x) = - +2,
-/+2, -2
2x - 3,
x22
Step-by-step explanation:
you don't show us all possible answer options.
none of the visible graphs are correct.
just look at x=0. g(0) = -0/2 + 2 = 2
so, the correct graph has to go through (0, 2). and the 3 segments connect at the interval end points
(-2, 3) and (2, 1).
so, please pick the correct answer option based on this information.
-x (y-8) ^2 for x = -2 and y = 5 ?
Box of clothes Weighting 10lbs (4.5kg) and a box of books weights 10lbs (4.5kg) was put on balance beam scales would most likely will it do
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.) 1 0 1 0 1 0 0 0 0 (x1, x2, x3) =
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
The matrix is:
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
The system of equations' equivalent augmented matrix is
[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]
The following matrix has been reduced and transformed into a set of equations.
x(1) + x(3) = 0
Subtract x(3) on both side, we get
x(1) = -x(3)
x(1) = -t
x(2) = 0
Let x(3) = t
[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
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The complete question is:
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
(x1, x2, x3) =
What will it cost to make 1,580 copies if the cost of 50 copies is $2.05
Answer:
=$64.78
Step-by-step explanation:
If. 50 copies. = $2.05
than. 1,580 copies = ?
1580/50 × $2.05
=3239/50
=64.78
Therefore if the cost of 50 copies is $2.05 than the cost of 1,580 copies is $64.78.
Answer:
$64.78
Step-by-step explanation:
Proportions:
50 copies >>>> $2.05
1580 copies >>>> $C
C = 1580"2.05/504
C = 64.78
Solve the equation.
2x² +6=-34
The solutions are x =
and x =
The solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
How to evaluate for the solution of the equation2x² + 6 = - 36
2x² = - 36 - 6 { subtract 6 from both sides of the equation }
2x² = - 40
x² = -40/2 {divide through by the coefficient of x² which is 2}
x² = -20
we take the square root of both sides
x = ± √-20
√-20 = √20 x √-1 { -1 = I an imaginary number}
so;
x = √20i or x = -√20i
Therefore, the solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
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Twenty members of an athletic club are studying the relationship between the time it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table.
TermCoefSE CoefTConstant39.884.249.41Time to fatigue3.920.715.52
Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
3.92±1.734(0.71)
The confidence interval for the slope of the regression line relating performance score is 0.71
sample size (n) = 20
slope (b1) = 3.92 and SE of slope = 0.71
Degrees of freedom = 20 - 2 = 18
Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,
tα/2=1.734
The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,
B1±Tα/2*SE
3.92±1.734(0.71) (c)
Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.
For example, how commodity prices relate to the shares of companies that trade in those commodities.
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A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed.
The city will have (blank) streetlights at the end of 46 weeks.
The city will have 232 streetlights at the end of (blank) weeks.
Answer:
316 street lights.
25 weeks.
Step-by-step explanation:
Linear Equations:We can set up a linear equation with the information provided expressed in slope intercept form: [tex]y=mx+b[/tex], where "m" is the slope, and "b" is the initial value.
We're given the initial amount, or what the city already has is 132 street lights, that's our "b" value and they will install 4 each additional week which is our slope. So we have the equation: [tex]y=4x+132[/tex]
To find how many streetlights the city will have at the end of 46 weeks, we can plug in 46 as "x" to give us:
[tex]y=4(46)+132\\y=316[/tex]
To find when the city will have 232 streetlights we can set the equation equal to 232 and solve for "x" the number of weeks.
[tex]232=4x+132[/tex]
Subtract 132 from both sides
[tex]100=4x[/tex]
Divide both sides by 4
[tex]25=x[/tex]
So this will occur after 25 weeks.
Find the slope of the line y=2x+17.
Answer:
Step-by-step explanation:
2x + y = 17 in slope intercept form? Put the y on one side by itself. -2 is the slope and 17 is the y-intercept. Slope / gradient of a line is obtained by making an equation in the form of: where ' m ' gives the slope/gradient of the line and ' c ' gives y-intercept.
The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y", this form is called "slope-intercept form" and the reason for that name is because it easily shows both the slope and the y-intercept of the line.
Check attached image 1 to better understand this concept.
As you may see in the picture, the slope is just the number that multiplies variable "x". Hence, the coefficient of this line is 2.
Check attached image 2 to see the graph of this line. Notice that the y-intercept is 17, as shown in the slope-itercept form of the equation.Jotham needs 18 liters of a 80% alcohol solution. He has a 30% and a 90% solution available. How many liters of the 30% and how many liters of the 90% solutions should he mix to make the 80% solution?
The amounts of each solution that he should use are given as follows:
30% solution: 3 liters.90% solution: 15 liters.How to obtain the amounts of each solution?The amounts of each solution are obtained by a system of equations, for which the variables are given as follows:
x: amount of the 30% solution.y: amount of the 90% solution.The total solution is of 18 liters, hence:
x + y = 18.
x = 18 - y.
The final concentration is of 80%, hence:
0.3x + 0.9y = 0.8 x 18
0.3x + 0.9y = 14.4.
As x = 18 - y, the value of y is obtained as follows:
0.3(18 - y) + 0.9y = 14.4
0.6y = 9
y = 9/0.6
y = 15.
Hence the value of x is obtained as follows:
x = 18 - y
x = 18 - 15
x = 3.
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HELPP!!
One rental store charges a one time fee of $12 plus $3 per hour to rent a power washer. A
second rental store charges $15 plus $2 per hour to rent a power washer. For what number
of hours is the rental cost the same?
Answer:
3 hours
Step-by-step explanation:
First, we need to set up an equation with a variable representing the time.
12 + 3x = 15 + 2x
Then you solve.
12 + 3x = 15 + 2x
-2x-12 -2x-12
x = 3
Need help ASAP will reward
Answer: 24.35333333
Step-by-step explanation:
6x x 6 + 75 = 10x - 9
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4. It's really common to contrast expressions and phrases.
what is expression ?It is necessary to duplicate, divide, add, or subtract in mathematics. The following is how an expression are put together: Number, expression, and mathematical operator The components of a numerical method include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It's really common to contrast expressions and phrases. An language, often known as an algebraic expression, is any mathematical statement that rating systems, numbers, and then an arithmetic function between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.
given
6x + 75 = 10x -9
Because 6x + 75 = 10x -9
6x -10 x = -9 - 75
-4x = -84
x = 21; the value of x is 4.
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4.
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Quadrilateral BCDE is shown on the coordinate grid. Keisha reflects the figure across the line y=x to create B’C’D’E’. Use the connect line tool to draw quadrilaterl B’C’D’E
The vertices of quadrilateral B'C'D'E' are obtained exchanging the x and y-coordinates of the vertices of Quadrilateral BCDE.
Then the quadrilateral is drawn connecting the four vertices of quadrilateral B'C'D'E'.
What is the reflection rule?The rule for a reflection over the line y = x is given as follows:
(x,y) -> (y,x).
Meaning that a reflection over the line y = x will exchange the coordinates of the figure.
Then we apply this procedure to obtain the vertices of quadrilateral B'C'D'E', and in the drawing connect the consecutive vertices.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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Which of these is the note A?
A.
OB.
O C.
O D.
Co
6.
fo
Answer:
the correct answer is A
Step-by-step explanation:
A correspond to Note La
Find the values of x , y and z .
Answer:
x = 144y = 60z = 156Step-by-step explanation:
Given two segment measures in a right triangle diagram, you want the values of the other measures.
Pythagorean theoremThe Pythagorean theorem can be used to find y:
BC² = BD² +CD²
65² = y² +25²
y² = 65² -25² = 3600
y = √3600 = 60
Similar trianglesThe proportionality of corresponding sides in similar triangles can be used to find the remaining measures.
short side/hypotenuse = 25/65 = 65/(25+x)
25 +x = 65²/25 = 169
x = 144
And for z, we can use ...
long side/hypotenuse = AB/AC = BD/BC
z/169 = 60/65
z = 169(12/13) = 156
The triangle measures are ...
x = 144y = 60z = 156six flags charges $35 per student, plus a $40 processing fee per group. If you graph this, where would the line cross the y-axis?
Answer: the line will cross the y-axis at (0, 40).
Step-by-step explanation:
the line of a function crosses the y-axis at the y intercept. to find the y-intercept, equal x to 0 in the slope intercept equation.
because we know that it is 35 per student and 40 processing fee per group, we know that the slope intercept equation is y = 35x + 40.
with the equation, we plug x in as 0 and solve for y.
y = 35(0) + 40
y = 0 + 40
y = 40
because we know the x-coordinate is 0, we now have the y-coordinate, which is 40.
therefore, the line crosses the y-axis at (0, 40)
solve the inequality |x| < 5
The inequality is solved to x < -5/4
What is an inequality?An inequality can be defined as a mathematical relation that makes a non-equal comparison between two numbers, mathematical expressions or equations.
Inequalities are used to compare two numbers on the number line on the basis of their size.
The different inequality signs are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that;
|x| < 3x - 5
Note that the signs, "| |" represents modulus which explains that the number must be a positive number.
collect like terms
x -3x< 5
substract the like terms
-4x< 5
Make 'x' the subject
x < -5/4
Hence, the value is x < -5/4
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The complete solution is:
solve the inequality |x| < 3x - 5
Please help me with the following question.
The probabilities for this problem are given as follows:
a) At least five: 0.4909 = 49.09%.
b) Less than five: 0.4091 = 40.91%.
c) Between five and ten: 0.585 = 58.5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 100, p = 0.05.
Hence the mean and the standard deviation of the approximation are given as follows:
Mean: [tex]\mu = 100 \times 0.05 = 5[/tex]Standard deviation: [tex]\sigma = \sqrt{100 \times 0.05 \times 0.95} = 2.18[/tex]Then the probability of at least five successes, using continuity correction, is P(X > 4.5), which is one subtracted by the p-value of Z when X = 4.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.5 - 5)/2.18
Z = -0.23.
Z = -0.23 has a p-value of 0.4091. (probability of less than five successes).
1 - 0.4091 = 0.4909 = 49.09%.
The probability of between five and ten successes is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 4.5, hence:
Z = (10.5 - 5)/2.18
Z = 2.52
Z = 2.52 has a p-value of 0.9941.
Z = (4.5 - 5)/2.18
Z = -0.23.
Z = -0.23 has a p-value of 0.4091.
Hence:
0.9941 - 0.4091 = 0.585 = 58.5%.
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Please help me with this question.
The complete solution to the system of equations in this problem is given as follows:
x = [-14; 5; 0; 2]
How to solve the system of equations?The system Ax = b is given in augmented matrix form, hence it is defined as follows:
[tex]x_1 + 3x_2 + 2x_3 + 2x_4 = 5[/tex][tex]2x_1 + 3x_2 - 2x_3 + 10x_4 = 7[/tex][tex]4x_1 + 13x_2 + 7x_3 - 3x_4 = 3[/tex][tex]3x_1 + 9x_2 + 5x_3 + 3x_4 = 9[/tex]Inserting the system into a calculator, the homogeneous solution is given as follows:
[tex]x_1 = -14, x_2 = 5, x_3 = 0, x_4 = 2[/tex]
The system has no given inputs, hence the particular solution is of zero.
Hence the complete solution in matrix form is given as follows:
x = [-14; 5; 0; 2]
(the ; separator means a new line).
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Write down the percentage multiplier to find 26% of an amount
pls do simple steps/working out :)
Answer:
To find 26% of an amount, you would use the percentage multiplier of 0.26.
Step-by-step explanation:
To use the multiplier, you would simply multiply the amount by 0.26.
For example:
26% of $100 = $100 x 0.26 = $26.
Alternatively, you can also express the percentage as a decimal by moving the decimal point two places to the left. In this case 26% is equal to 0.26
So, to find 26% of an amount you would multiply the amount by 0.26
For example:
26% of $100 = $100 x 0.26 = $26.
Find the area of the sector of the circle with central angle of 195° and radius of 7 cm. Use 3.14 for pi(π) and round to the nearest hundredth.
Group of answer choices
23.81 cm2
166.68 cm2
27.86 cm2
83.34 cm2
Answer:
A ≈ 83.34 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{195}{360}[/tex] ( r is the radius of the circle )
= 3.14 × 7² × [tex]\frac{13}{24}[/tex] ( cancelling by 15 )
= [tex]\frac{3.14(49)(13)}{24}[/tex]
≈ 83.34 cm² ( to the nearest hundredth )
Researchers wanted to determine if a new organic pesticide Z was effective at killing grasshoppers that typically invade cornfields. The effect of the grasshoppers in the fields is a decrease in yield which has economic consequences on the farmers. For the study two ten-acre cornfields located 1 mile apart were chosen. The cornfield to the west was sprayed only with water. The cornfield on the east received the same amount of water with a 10% solution of organic pesticide Z. Samples of the numbers of grasshoppers in the field were made every week for 10 weeks.
RESULTS
West field treated only with water
The number of grasshoppers in the west field doubled after ten weeks.
East field treated with pesticide Z
The number of grasshoppers in the east field declined by 50% after 10 weeks.
The following questions relate to this experiment.
1) State a possible hypothesis for this study. 2) What was the purpose of conducting this experiment? 3) What was the independent variable in the above experiment? 4) What was the dependent variable in the above experiment? 5) Which group was the control group? 6) Why is it important to have a control group in the experimental design? 7) Which of the following is the most accurate conclusion about these results?
Pesticide Z is a good way to control most insect infestations on fields of corn, wheat, or oats. East fields are more likely than west fields to have problems with grasshoppers eating corn crops. If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later. Pesticide Z is unable to kill grasshoppers and is not suitable for the use in modern agriculture. 8) Based on the results of the experiment what will be your recommendation to the farmer in order to decrease the number of grasshoppers in the cornfield. 9) Arrange the stages of the scientific method listed below in order from first to last. Analyze data Formulate hypothesis Make observation about nature Reject or accept hypothesis Conduct experiments 10) You have noticed that after you forget to water your houseplant it wilts. This is an example of which part of the scientific method:
a. Hypothesis b. Observations c. Experiment
A possible hypothesis for this study is: "The organic pesticide Z will reduce the number of grasshoppers in cornfields compared to water treatment alone."
The purpose of conducting this experiment is to determine if the new organic pesticide Z is effective at killing grasshoppers that typically invade cornfields and to study its effect on reducing the number of grasshoppers.
How to explain the variablesThe independent variable in the experiment is the treatment with organic pesticide Z.
The dependent variable in the experiment is the number of grasshoppers in the cornfield.
The west field treated only with water is the control group.
It is important to have a control group in the experimental design because it provides a baseline comparison for evaluating the effect of the treatment.
The most accurate conclusion is: "If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later."
Based on the results, my recommendation to the farmer would be to spray the cornfield with pesticide Z to decrease the number of grasshoppers in the cornfield.
The stages of the scientific method in order from first to last are: Make observations about nature, formulate hypothesis, conduct experiments, analyze data, reject or accept hypothesis.
This is an example of making observations about nature.
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EASY POINTS!
What is the total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost?
$9.60
$172.93
$72.93
$159.60
Answer:
The total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost would be $159.60. To calculate this, multiply the original cost by 1.064, which is the amount of the sales tax in decimal form. For example, if the original cost was $150, then the total cost would be $150*1.064 = $159.60.
