The common multiple of 14 and 28 is 28.
Common multiple:
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.
Here we have to find the common multiple of 14 and 28.
Data given:
Two numbers = 14 and 28
We can also write these numbers as:
14 = 2 × 7
28 = 2² × 7
The common multiple of these numbers is 2² × 7
Therefore the common multiple of these numbers is 28.
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Which is a solution of the equation 3x 14 4?.
Solution of the equation 3x - 14 = 4 will be x=6
What are Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
3x - 14 = 4
⇒3x = 4 +14 (adding 14 on both side)
⇒x = 18 / 3 (dividing 3 from both sides)
⇒x = 6
Hence, Solution to the equation 3x - 14 = 4 will be x=6
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at a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. for which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?
The Population set for a sample of 28 percent is a reasonable estimate sample of the percentage of those who have taken one or more courses in statistics is "all mathematics teachers who have taken one or more courses in statistics".
So, Correct option is option (C) .
We have given that ,
There is a large conference of teachers from a variety of subjects.
Random sample size = 50 mathematics teachers who attended the conference is selected.
Population set : A population is the entire group that you want to draw conclusions about, that is here population set contains all teachers who attand the conference .
Sample : It is defined as subset of population set in a representative manner. It is taken from large population.
here, sample is 50 selected mathematics teachers.
On reading the provided data we conclude that The required population set for given sample is All mathematics teachers who have taken one or more course in statistics.
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Complete question:
At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?
A. All mathematics teachers
B. All mathematics teachers who attended the conference
C. all mathematics teachers who have taken one or more courses in statistics
D. All teachers who attended the conference
E. All teachers
Exercie 8. 1 2. In a computer lab there are 3computer for every 6 tudent. How many computer will be needed for 24 tudent?
12 computers are required for 24 students in the computer lab.
We will be using the unitary method for solving a problem.
The unitary method is used to find the value for 1 unit and then find value the value of desired units accordingly.
Suppose there are 12 apples in 3 boxes.
Then we will first find no of apples in 1 box after that we can no of apples in as many boxes as we want.
No computers for 6 students = 3
No of computers for 1 student = 3/6
No of computers for n students = (No of computers for 1 student)*(No of students)
No of computers for 24 students = (3/6)*(24) = 12 computers
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A translation moves P(0,5) to P'(3,1). What are the coordinates of the image * 1 point
of point (-3,-5) under the same translation?
(0, -9)
(-5,-3)
(-6, -1)
(-6, -9)
To move P to P':
the x-coordinate increased by 3 units
the y-coordinate decreased by 4 units
Applying that translation to (-3,-5), we'd have (-3 + 3, -5 - 4) or (0,-9).
The first answer is correct.
Suppose A is a 2×2 real matrix with an eigenvalue λ=1+5i and corresponding eigenvector v⃗ =[−1+ii]. Determine a fundamental set (i.e., linearly independent set) of solutions for y⃗ ′=Ay⃗ , where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. y⃗ 1(t)= y⃗ 2(t)=
λ = 1 + 5i and ∨ = [ -1 + i , i ]
The first solution is[tex]y(t)=e^{\lambda t}\eta^1=e^{(1+5i)t}\begin{bmatrix} -1+i\\ i \end{bmatrix}\\y(t)=e^{t}(e^{5t}\begin{bmatrix} -1+i\\ i \end{bmatrix})[/tex]
Expanding the e^((5t)i) by Eulers Formula[tex]y(t) e(cos(5t) isin(5t) \begin{bmatrix} -1+i\\ i \end{bmatrix}\\\\y(t)=e^t\begin{bmatrix} (cos(5t)i+i^2sin(5t))-(cos(5t)+isin(5t))\\ cos(5t)i+i^2sin(5t)) \end{bmatrix}\\y(t)=e^t\begin{bmatrix} (-sin(5t)-cos(5t)+(cos(5t)-sin(5t))i\\ -sin(5t)+(cos(5t))i \end{bmatrix}[/tex]
Write the above solution x+yi[tex]y(t)=\left ( e^t \begin{bmatrix} -(sin(5t)+cos(5t))\\ -sin(5t) \end{bmatrix} \right )+\left ( e^t\begin{bmatrix} (cos(5t)-sin(5t))\\ cos(5t) \end{bmatrix} \right ) i[/tex]
The solution of the DE are[tex]y_{1}(t)= -e^t \begin{bmatrix} sin(5t)+cos(5t)\\ sin(5t) \end{bmatrix}\ and \ y_{2}(t)= e^t\begin{bmatrix} cos(5t)-sin(5t)\\ cos(5t) \end{bmatrix}[/tex]
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the othes solution in this picture: ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
The equation that can be used to find the width, w, of the rectangle with the given area is 2w² - w - 91 = 0
To determine the equation that can be used to find the width we use the following formula; Area of a rectangle = length × width
Since the area of the rectangle is 91 square inches and the length of the rectangle is 1 less than twice its width, this can be represented as;
Length of the given rectangle = 2w - 1
Using the area formula the equation to find the width would be:
(2w - 1)(w) = 91
2w² - w - 91 = 0
Hence 2w² - w - 91 = 0, is the equation that can be used to find the width.
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Suppose X1,X2,X3 are random variables, each with expected value mand variance v, and cov(Xi,Xj) = c, i not equal j. Calculate the covariance and correlation coefficient of U,V , where U = 2−X1−2X2, and V = 3+3X2−X3.
To calculate the covariance and correlation coefficient of U and V, we need to first find the expected value and variance of U and V.
What is covariance?The covariance of two variables is a gauge of their relationship. In other words, it is a measure of how much the values of two variables tend to fluctuate together. Positive covariance shows that the values of the two variables tend to rise or decrease together, whereas negative covariance indicates that the values of one variable tend to increase when the values of the other variable drop. In probability theory and statistics, covariance is frequently employed to determine the association between two variables. It is determined by multiplying the variances of the two variables from their respective means and dividing the result by the total number of observations. This metric can be helpful for seeing trends and patterns in data and aiding analysts in forecasting.
How to solve?
The expected value of U is $E[U] = E[2 - X_1 - 2X_2] = 2 - m - 2m = -2m. Similarly, the expected value of V is $E[V] = E[3 + 3X_2 - X_3] = 3 + 3m - m = 4m.
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To calculate the value of covariance and correlation coefficient of U and V, we have to find their expected value along with variance.
What does covariance mean?A measure of the link between two random variables and how much they fluctuate together is called covariance. Alternately, we may say that it establishes the relationship between the two variables' changes, i.e., that a change in one variable is equivalent to a change in the other.
What does the covariance tell us?When one variable changes, covariance shows the link between the other two variables. Both variables are said to have positive covariance if a rise in one causes an increase in the other. Reduced values of one variable also result in reduced values of the other.
for expected value of U ;
= $E[U]
= E[2 - X_1 - 2X_2]
= 2 - m - 2m = -2m.
Similarly, the expected value of V;
= $E[V]
= E[3 + 3X_2 - X_3]
= 3 + 3m - m
= 4m.
now we can easily calculate the covariance and correlation coefficient of U,V.
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Pls find 15 - 1/6n = 1/6n
Answer: 45
Step-by-step explanation:
15 - 1/6n = 1/6n
1. multiply everything by 6
90 - n = n
2. add n to the right-side
90 = 2n
3. divide
n = 90/2
n = 45
Frequent food questionnaires (FFQ) are a simple way to obtain information on the foods individuals consume by asking them questions about typical amounts of food consumed in a day or week or month. A more accurate picture is obtained by obtaining a detailed food diary (DR) for several days, randomly chosen over a certain time period. The data obtained from a frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire. The correlation between alcohol consumption from the food questionnaire and diary was r = 0.89 based on seven individuals. Based on the seven individuals for whom data is available, which statement is INCORRECT?DR8.26FFQ1.680.83020.1315.111.167.497.1812.841.76022.6625.06All of the answer options are correct.Because r > 0, the amount that is truly consumed is always larger than what is stated on the FFQ.Typical consumption as stated on a FFQ is positively associated with what is actually consumed.The FFQ is a reasonable tool to obtain information on the amount of alcohol consumed by individuals.
The amount the is truly consumed is always larger than what is stated on the FFQ. Hence, it is the incorrect statement for the indicated correlation.
What is correlation?
To represent the relationship between continuous variables, correlation is utilized. A numerical value called the correlation illustrates the connection between two variables. The sign affects the kind of relationship that exists between the variables. A direct or positive association would result if the sign is positive. It would be detrimental otherwise.
The correlation is a number which indicates relationship between two variables.
A correlation is used to test the relationship between continuous variables.
A correlation coefficient has a value between -1 and 1 this means there is a perfect negative or positive correlation. These are very high correlation examples.
A positive correlation does not imply that what is truly consumed is always larger than what is stated on the FFQ.
A positive correlation coefficient only implies that with a change in diary readings, the food questionnaire reading will also change in the same manner.
However, this does not reflect anything on the true consumed values and therefore, it cannot be judged whether the truly consumed amount will be larger or not.
The provided options are analyzed by the fact that the positive correlation means the change in the variables is direct rather than indirect.
The positive correlation means the direct change in the variables. Hence, the option is an incorrect one.
The correlation only represents whether the two variables have a positive or negative relationship. It does not tell anything about whether one value is greater or not.
Since, r > 0 the amount the is truly consumed is always larger than what is stated on the FFQ.
Hence, it is the incorrect statement for the indicated correlation.
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Lora's phone records data for screen time each week. Last week, she used 750 minutes. This week, lora used 495 screen time minutes on the phone. Calculate the percent decrease in screen time this week.
If this week, Lora used 495 screen time minutes on the phone. So the percent decrease in screen time this week is going to be 52%.
How can we determine the percent decrease?Using this formula to find the percent decrease
Percent decrease = Last week screen time - This week screen time / This week screen time
According to the question :
Last week screen time = 750 minutes
This week screen time = 495 minutes
Lets substitute the values in the formula ,
Percent decrease = 750 - 495 / 495
Percent decrease = 255 /495 × 100
Percent decrease = 51.5%
Percent decrease = 52% (Approximately)
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The two polygons are similar, find the missing length. (the ?)
The required measure of the missing length is given as 14 units.
Given that,
The figure of two similar triangles is given, and the missing length of the figure is to be determined.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Let the missing length be x,
So by property of proportions,
20/8 = [49 - x] / x
20x = 392 - 8x
28x = 392
x = 14
Thus, the required measure of the missing length is given as 14 units.
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autotrader would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. the following data represent the age of a random sample of trucks, cars, and vans. trucks cars vans 12 8 3 8 7 7 9 10 6 11 7 8 the grand mean for these observations is .
The grand mean for these observations is 8.
What is the grand mean in statistics?
The grand mean, also known as the pooled mean, is the average of the means of several subsamples with the same number of data points.
The given data is:
12, 8, 3, 8, 7, 7, 9, 10, 6, 11, 7, 8.
The sum of all these observations = 12 + 8 + 3 + 8 + 7 + 7 + 9 + 10 + 6 + 11 + 7 + 8 = 96.
A total number of observations = 12.
Grand mean = Sum of all these observations/Total number of observations
= 96/12
= 8
Hence, the grand mean for these observations is 8.
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A Three integers have a mean of 10, a median of 12 and a range of 10. Find the three integers.
Answer:
4 , 12 , 14
Step-by-step explanation:
1) We are told that the median (middle number) is 12 and that the mean is 10
This means that the numbers added together, divided by 3 which equals to ten. From this we can understand that the numbers should add up to 30 as 30 divided by 3 is 10
2) We already know one of the middle numbers which is 12 so the next step would be to subtract 12 from 30 which would be 18.
3) We are also told that the range is 10 meaning that the difference between the smallest and biggest number is 10. If the difference between the smallest and biggest is 10 and the number that they can add to is 18, all we have to do to get our numbers subtract 10 from 18 which is 8 and divide it by 2 which is 4. We have to divide it because we need to find two more numbers
4) From the information we have so far we know that one of our numbers is 4 and the other is 12. To get the final number, add 12 and 4 together which is 16, and subtract that from 30 which is 14. Meaning our numbers are 4 , 12 and 14
5) To check if this is right we can see that the range is 10 (14 - 4 = 10) the mean is 10 (4 + 12 + 14 = 30) and the median is 12!!
Hope this helps, have a great day!
Jacob wants to buy a $500,000 15-year term life policy, and the annual premium rate (per $1000 of face value) for his age group is $6. 78. If jacob lives until the end of the term of his policy, how much will jacob have paid in premiums overall? a. $101,700 b. $3,390 c. $50,850 d. $73,746 please select the best answer from the choices provided a b c d.
The required annual premium rate for the given term life policy is $50,850.
Explain term life policy and annual premium rate.Term life insurance covers you for a particular measure of time - basically, the strategy's term. The length of the term can change to suit your specific conditions. You can likewise look over two changed sorts of term disaster protection: diminishing term protection and level term protection.
annual premium rate:Annual Premium Rate implies, if pertinent, the exceptional rate so determined on the Statements Page of this Strategy to be utilized in processing a premium to be transmitted yearly.
According to quetion:Jacob needs to purchase a $500,000 15-year term life strategy, and the yearly superior rate (per $1000 of presumptive worth) for his age bunch is $6. 78.
Number of 1000 of every 500000 will be 500000/1000 = 500
the yearly superior rate (per $1000 of assumed worth) for his age bunch is $6. 78.
Absolute premium is 500 x 6.78 = 3390
The premium each year is 3390
For quite some time, the all out premium is
15 x 3390 = 50850
Thus, over all premium jacob have paid $50850.
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Which parent function is represented by the graph straight line?.
A linear function is represented by the graph straight line.
In the given question we have to explain which parent function is represented by the graph straight line.
As we know that;
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
There are several basic functions that we run with frequently in math. These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.
A linear function with a degree of one that is linear and expressed as f(x)=x. f(x) = x, where the function's graph passes through the origin, is referred to as a linear function.
Hence, a linear function is represented by the graph straight line.
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1.a telephone company is asked to provide service to a customer whose house is located in the forest, 900 feet away from the road along which the phone lines run. the nearest telephone box is located 4,200 feet down the road. the cost to install the phone line is $20per foot along the road and $35 per foot away from the road (through he forest).
In total, the cost to install the phone line for the customer in the forest will be $31,500+$84,000=$115,500.
What is meant by addition?Combining two or more numbers or quantities to generate a sum is known as addition in mathematics. One of the four fundamental operations of arithmetic, along with addition, subtraction, multiplication, and division, it is often denoted by the sign "+."
Addition is a key concept that is taught to children at an early age and is utilised in a number of everyday settings such as shopping and banking. It is a crucial tool for tackling increasingly difficult issues in disciplines like engineering, physics, and finance. For example, a telephone company is asked to provide service to a customer whose house is located in the forest, 900 feet away from the road along
Mental computation, pencil and paper, and calculators are only a few of the techniques that may be used to do addition. First, arrange the digits in columns, starting with the ones place, before adding two numbers.
How to solve?
To provide service to the customer in the forest, the telephone company will have to run a phone line 900 feet through the forest at a cost of $35 per foot, for a total cost of 900*$35=$31,500.
Additionally, the company will have to run the line 4,200 feet down the road at a cost of $20 per foot, for a total cost of 4,200*$20=$84,000.
In total, the cost to install the phone line for the customer in the forest will be $31,500+$84,000=$115,500.
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During a four week period you work the following hour
Week 1: 36 3/8
Week 2: 41 1/4
Week 3: 40 1/2
Week 4: 38 3/8
What i the average number of hour you worked in one week?
You work an average of 39 1/8 hours per week.
The given can be used to calculate the average.
(36 3/8 + 41 1/4 + 40 1/2 + 38 3/8) / 4 =
36 + 41 + 40 + 38 = 155
3/8 + 1/4 + 1/2 + 3/8 = 3/8 + 2/8 + 4/8 + 3/8 = 12/8 = 1 1/2
155 + 1 1/2 = 156 1/2
(156 1/2) / 4 =
313/2 * 1/4 = 313/8 = 39 1/8
average weekly hours are 39 1/8.
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find the area of the triangle below. carry your intermediate computations to at least four decimal places. round your answer to the nearest hundredth.
The area of the given triangle is 20 square kilometers.
Here, we are given a triangle as shown in the figure below.
There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-
area of triangle = 1/2 × sinФ × side 1 × side 2
where, Ф = angle formed by side 1 and side 2
Here, Ф = 35
Sin 35 = 0.5736
Thus, the area of the triangle will be-
1/2 × 0.5736 × 7 × 10
= 35 × 0.5736
= 20.076
20.076 rounded off to nearest hundredth is 20
Thus, the area of the given triangle is 20 square kilometers.
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Your question was incomplete. Check for the missing figure below
When beth was 9 years old, paul was 3 times younger than her. Now beth is 30 years old, how old is paul?.
Step-by-step explanation:
9÷3=3 so when beth is 30 you need to do 30-6 which is 24
When beth was 9, paul was 3 times younger = 9/3 = 3 years old.
Beth has gained 21 years since, so the age of paul is 3 + 21 = 24 years old.
SOMEONE PLS PLS PLS ANSWER THIS. I’ve been asking this question since last week T-T
Only answer if you KNOWWW. !
What goes on the boxes ??
The system of equations have infinitely many solutions and the solutions can be n = 2, d = 5, y = -1 and n = 2, d = 5, y = -1
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear equations in three variables are shown in the picture.
The linear equations are represented in a matrix form.
After solving we will get:
u = 23n/33 - d/3 - 8/11
u = 5n/6 - d/3 - 1
u = 2n/3 - d/3 - 2/3
n = 2
d = 3x + 2
u = -x
Where x is any number
Plug x = 1
n = 2
d = 5
y = -1
Plug x = 2
n = 2
d = 5
y = -1
Thus, the system of equations have infinitely many solutions and the solutions can be n = 2, d = 5, y = -1 and n = 2, d = 5, y = -1
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Write an equation of a line in lope-intercept for that i perpendicular to the line y=1/2x-5 and pae through the point (1, -2)
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
to find the slope of the target line we use the slope of the given line : 1/2.
remember, the slope is expressed as ratio (y coordinate change / x coordinate change).
the given line increases the y- value by 1, when the x-value increases by 2.
a perpendicular slope (90°) simply turns y and x upside-down and flips the sign.
so, 1/2 turns into -2/1 = -2.
so, we see our line equation looks like
y = -2x + b
to get b we use the coordinates of the given point :
-2 = -2×1 + b
-2 = -2 + b
0 = b
so thar equation is simply
y = -2x
What are the coordinates of the point on the directed line segment from (−9,−6) to (−2,1) that partitions the segment into a ratio of 3 to 4?
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-9,-6)\qquad B(-2,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:4} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{4}\implies \cfrac{A}{B} = \cfrac{3}{4}\implies 4A=3B\implies 4(-9,-6)=3(-2,1)[/tex]
[tex](\stackrel{x}{-36}~~,~~ \stackrel{y}{-24})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{3}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-36 -6}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-24 +3}}{3+4} \right)} \\\\\\ C=\left( \cfrac{ -42 }{ 7 }~~,~~\cfrac{ -21}{ 7 } \right)\implies \boxed{C=(-6~~,~~-3)}[/tex]
What is the domain of the square root function graphed?.
The domain of the square root function is x≥0.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.
To find out a perfect square we need to find out square root is an integer.
Hence, The domain of the square root function is x≥0.
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A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject Do not reject What is the p-value? (Round your answer to 4 decimal places.)
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis on coducting a one tail test.
What is Hypothesis?A hypothesis is a theory put up to explain a phenomena. A link between two or more variables is described, and the proposition is testable. A hypothesis is an informed estimate or forecast made before undertaking any tests or research to determine its validity. A strong hypothesis should be definable, testable, and supported by prior data. It should also be stated in a way that allows it to be disproven, so that it can be tested using empirical evidence. Generally speaking, a hypothesis serves as the basis for additional research and testing in a scientific endeavour.
How to solve?
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis if the test statistic is less than -1.96.
To calculate the test statistic, we use the formula:
z = (x - μ) / (s / √n)
x = 215, μ = 220, s = 15, and n = 64. Plugging these values into the formula gives:
z = (215 - 220) / (15 / √64) = -5 / (15 / 8) = -5 / 1.875 = -2.67
The test statistic is -2.67, which is less than the critical value of -1.96, so we reject the null hypothesis.
To calculate the p-value, we can use the z-table to look up the area under the normal curve that is to the left of -2.67. This area is approximately 0.0031, which is the p-value.
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis.
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle then the triangles are said to be congruent?.
It is said to be in AAS or ASA congruency when two angles and a side from one triangle match the corresponding area of another triangle.
What do we mean by ASA congruency?The Angle-Side-Angle Postulate (ASA) states that two triangles are congruent if both of their included angles and two of their included sides are present in the other triangle.Additionally, we prove the Angle-Side-Angle Postulate, as shown in the right image, that triangles ABC and DEF are congruent.AAS congruency:
On the other hand, according to the AAS (Angle-Angle-Side) postulate, two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another.The Angle-Angle-Side Postulate is used to demonstrate the congruence of triangles ABC and QPR.Therefore, it is said to be in ASA or AAS congruency when two angles and a side from one triangle match the corresponding area of another triangle.
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Which linear equations have an infinite number of solutions?.
Linear equations have an infinite number of solutions are-
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 8 = 3(–6 + 4.1x)
What is Linear equations?
A linear equation is an equation within which the very best power of the variable is usually one.
Main body:
A linear equation can be said to have an infinite number of solutions when the number of the right hand side is the same at the number on the left hand side of the equation.
For example:
2 = 2 or x = x or 0 = 0
Solving the question above:
Which linear equations have an infinite number of solutions? Check all that apply.
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
x - 3/7 = 6x/6 - 18/42
x - 3/7 = x - 3/7
Collect like terms
x - x = -3/7 + 3/7
0 = 0
The linear equation in option a has an infinite number of solutions
b) 8(x + 2) = 5x – 14
8x + 16 = 5x - 14
Collect like terms
8x - 5x = -14 - 16
3x = -30
x = -30/3
x = -10.
The linear equation in Option b has a true solution.
c) 12.3x – 18 = 3(–6 + 4.1x)
12.3x - 18 = -18 + 12.3x
Collect like terms
12.3x - 12.3x = -18 + 18
0 = 0
The linear equation in Option c has infinite number of solutions
d) 1\2(6x + 10) = 7(3\7x – 2)
6x/2 + 5 = 21/7x - 14
3x + 5 = 3x - 14
Collect like terms
3x - 3x = -14 - 5
0 = -19
The linear equation Option d has no solution
e) 4.2x – 3.5 = 2.1 (5x + 8)
4.2x - 3.5 = 10.5x + 16.8
Collect like terms
4.2x - 10.5x = 16.8 + 3.5
-6.3x = 20.3
x = -20.3/6.3
x = -3.22
Hence, the linear equation in Option e has a true solution
Therefore, the linear equations have an infinite number of solutions are:
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 18 = 3(–6 + 4.1x)
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Over the summer, paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. Weekly revenue and expenses revenue expense sales $124 supplies $8 he works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?.
16 weeks would pass before any further dogs need to be bathed.
Define the term profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.The parameters being:
Initial investment = $32Eight weeks were worked.From the formula;
Profit = Sales - Expenses.
Weekly profit is $124 - $8 = $116.
Total revenue generated:
Number of weeks Profit per week.:
= $116 × 8
= $928
Total ownership is total revenue plus initial investment.
Owned in total:
$928 + $32 = $960.
The number of weeks until the entire amount owned is spent can be computed as follows:
Total amount owned weekly spending
= ($960 / $60) = 16
Thus, 16 weeks would pass before any further dogs need to be bathed.
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In a certain fraction, the denominator is 4 larger than the numerator. If 2 is added to both the numerator and the denominator, the result is 3/5. Find the original fraction.
The value of the original fraction is found as 4/8.
Explain the term fraction?A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator and denominator of a complex fraction. The numerator of a proper fraction is less than denominator.Let a be the numerator.
Let b be the denominator.
B = A + 4 has a denominator 4 times larger than a numerator.
Both the numerator as well as the denominator receive an addition of 2: (a + 4 + 2) and a + 2.
The following algebraic equation is created from the provided statement:
(a + 2)/(a + 4 + 2) = 3/5
(a + 2)/(a + 6) = 3/5
5(a + 2) = 3(a + 6)
5a - 3a = 18 - 10
a = 4
Put the value of a in the original fraction;
a/ (a + 4) = 4/(4 + 4)
= 4/8
Thus, the value of the original fraction is found as 4/8.
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consider running golden section search on a function that is unimodal. if the method starts with an initial bracket of , what is the length of the bracket after 1 iteration?
The length of the bracket after 1 iteration is 100%.
Let f(x) = x³-15x² + 50x
a = 0, b=10.
Let the golden ratio be
GR=√5-1 / 2=0.618
Now, d = GR (b-a)
= 0.618 (10-0) = 6·18
[tex]x_{1}[/tex]= a+d = 0 + 6·18 = 6.18
[tex]x_{2}[/tex] = b-d = 10- 6·18 = 3.82
f([tex]x_{1}[/tex]) = (6·18)³ - 15 (6·18)² + 50(6·18) = -27.887
f([tex]x_{2}[/tex]) = (3.82)³-15(3.82)²+50(3.82)=27.857
so, f([tex]x_{2}[/tex]) > f([tex]x_{1}[/tex]) new interval is [a,x,]
i.e., maximum lies in [0, 6·18]
so, Xmax = [tex]x_{2}[/tex]= 382
Uncertainty in measurement will be,
∈= [tex]\frac{1-GR) (b-a)}{Xopt}[/tex] =[tex]\frac{((1-0.618) X (10-0)}{382}[/tex] × 100%
∈ = 100%
In arithmetic, quantities are within the golden ratio if their ratio is the same as the ratio in their sum to the larger of the 2 portions. Expressed algebraically, for quantities a and b with [tex]a > b > 0[/tex], [tex]\frac{(a+b)}{a}[/tex] = [tex]\frac{a}{b}[/tex]= φ
The golden ratio turned into known as the acute and suggest ratio by way of Euclid, and the divine proportion using Luca Pacioli, and also is going through numerous other names. The golden ratio seems in some patterns in nature, such as the spiral association of leaves and different elements of plants.
A few twentieth-century artists and architects, together with Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing them to be aesthetically appealing. these uses often appear in the form of a golden rectangle.
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a child enters a carousel that takes one minute to revolve once around. the child enters at the point (0,1) , that is, on the due north position. assume the carousel revolves counterclockwise. what are the coordinates of the child after 15 seconds?
The required position of the child after 15 seconds of revolution.
What is carousel ?The word merry go round began from the Italian Carousel and Spanish Carousel ("little fight", utilized by crusaders to portray a battle readiness exercise and game played by Turkish and Bedouin horsemen in the twelfth hundred years).
According to question :A child enters at (0, 1) that is, on the due north position.
As it says the carousel revolves counterclockwise.
1 minute = 60 seconds = one round
rounds revolve in one second = 1/60 rounds
Then rounds in 15 seconds = 15/60 = 1/4 = 0.25
Thus, point after 15 seconds is (-1, 0).
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