For the given scatter plot of the data, the wrong with the conclusion was shown by option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect.
As given in the question,
Based on the class data of quiz3,
Teacher made scatterplot to represent the linear relation between amount of study time and quiz score
Pattern form was linear.
Using which correlation coefficient was computed to r = 0.8.
From the data scatterplot as it was linear the more time students study the good will the score.
Therefore, from the information of scatterplot option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect answer.
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A graphing calculator is recommended.
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)
Weights of Student Lab Rats
Linda's rats Tuan's rats Javier's rats
46.3 49.8 53.3
42.3 42.7 43.1
44.1 41.8 40.2
48.7 48.9 47.7
40.8 46.5 51.5Enter an exact number as an integer, fraction, or decimal.
df(num) =
Enter an exact number as an integer, fraction, or decimal.
df(denom) =
State the distribution to use for the test.
A. F2, 12
B. F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
A. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
B. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
C. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
D. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
(ii) Decision:
reject the null hypothesisdo not reject the null hypothesis
(iii) Reason for decision:
Since α < p-value, we do not reject the null hypothesis.
Since α > p-value, we reject the null hypothesis.
Since α < p-value, we reject the null hypothesis.
Since α > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
The graph representation of the given distribution is attached below.
The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.
Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.
Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :
=> F=0.66853555
=> p = 0.530548
And the FACTOR df =2 and SS=23.212
=> MS = 11.606
Here the ERROR df = 12
=> SS=208.324
=> MS = 17.36
Here by using the f distribution for the test of three different means.
Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301
When we plot the graph for the distribution then we get he graph like the following.
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Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
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HELP ASAP
3. If the aspect ratio of a tire is 50%, width 10 inches, and the rim diameter is 19 inches, what is the tire diameter?
a. 59in b. 35.8in
d. 49in
4. The standard print paper is 11" by 8.5 in. What is the aspect ratio of a standard print paper?
a. 11:8
c. 8.5
c. 29 in
b. 22:17
d. 11
3) The tire diameter using the aspect ratio is; 29 inches
4) The aspect ratio of a standard print paper is; 22:17
How to solve aspect ratio problems?The aspect ratio is defined as the relationship between the width and height.
Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;
3) We are told that the aspect ratio of a tire is 50%.
Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.
Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches
4) The standard print paper is 11" by 8.5. This can also be written as;
11 by 17/2 or 11 * 2 : 17
= 22:17
This then gives us the aspect ratio.
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2(x - 6) + 2 = 4x - 4
Answer:
x = - 3
Step-by-step explanation:
2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify
2x - 12 + 2 = 4x - 4
2x - 10 = 4x - 4 ( subtract 4x from both sides )
- 2x - 10 = 4x - 4 ( add 10 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer:
SOLUTION
2(X-6)+2=4X-4
open the blanket by multiplication
2x-12+2=4x-4
2x-10=4x-4
collect like term
2x+4x=-4+10
6x=6
divide both side by 6
x=1
an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
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for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
What is a T test?A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.
The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.
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Complete question
for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
a. a weighted average of the two sample
b. the difference between the standard deviationa
c. The variance
d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
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The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
find two polynomials whose difference is 2x^2 + x + 4
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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Daniel ran 5 kilometers less then Abhasra last week. Daniel ran 16 kilometers. how many kilometers did Abhasra run?
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
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What is the product?
2•[-1]
[0]
Answer:
-2
Step-by-step explanation:
PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft
How to determine the length of the side length AYFrom the question, we have the following parameters that can be used in our computation:
BC = 16.7 ft
The measures of the angles are not given
However, the marks on the side lengths imply that:
The points A, B and C divides the line segments XY, XZ and YZ into equal segmentsThe parallel segments are equal segmentsUsing the above as a guide, we have the following:
AY = BC
This is because these segments are parallel segments
Recall that parallel segments are equal segments
Substitute the known values in the above equation, so, we have the following representation
AY = 16.7
Hence, the length of AY is 16.7 ft
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Given the points (1, -4) and (4, 5), construct two equations in point slope form using each of the points. Construct and upload the graph of the line. Show your work and upload your graph for your teacher to review.
The equation of line passes through the points (1, -4) and (4, 5) will be;
⇒ y = 3x - 7
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, -4) and (4, 5).
Now,
Since, The equation of line passes through the points (1, -4) and (4, 5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-4)) / (4 - 1)
m = 9 / 3
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - (-4)= 3 (x - 1)
⇒ y + 4 = 3x - 3
⇒ y = 3x - 3 - 4
⇒ y = 3x - 7
Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;
⇒ y = 3x - 7
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Age of Senators The average age of senators in the 108" Congress was 57.5 years. If the standard deviation was 11.5 years, find the -scores corresponding to the oldest and youngest senators of age 87 and 44. Round scores to two decimal places. find the z-score corresponding to the oldest senator of age 85 is
The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex]. Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.
Given μ = 57.5 and σ = 11.5.
When x = 87, the z-score value is,
[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]
When x = 44, the z-score value is,
[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]
When x = 85, the z-score value is,
[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]
The required answers are 2.57, -1.17, and 2.39.
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Graph the solution of the inequality on a number line.
2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5
Answer:
Choice D : x > - 1
Step-by-step explanation:
Left hand side (LHS) of the inequality can be siimplified
[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]
Inequality becomes
[tex]-3x-6 < x-2[/tex]
Move x to the left side and -6 to the right side:
[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]
Multiply both sides by -1(the inequality sign changes to >)
[tex]4x > -4\\\\[/tex]
Divide both sides by 4:
[tex]x > -1[/tex]
The number line corresponding to this is the fourth choice
A reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours. If the tank originally contained 200 gallons of coolant, approximately how many gallons are in the tank after 8 hours?
The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
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Keisha and David each found the same value for cos0, as shown below, given sin0=-8/17. Keisha's Solution
tan²8+1 = sec²e
sin² e
cos² e
=+1=
17
cos² e
(-) + Co
+1=
1
cos² e
cos² e
+ cos²9=1
64
cos 9-1-
-- 289
15
cose=17
David's Solution
sin²+ cos² = 1
cos²8-1-(-17)
Со
cos = ±
225
289
15
cose=¹17 whose procedure is correct?
The procedure is correct is 1 + tan²(theta) = sec²(theta)
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Keisha and the David.
As per the question Kisha and the David found the same value of the cosine theta as given by the Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).
Thus the answer is both procedures are correct.
As they both wanted to find the solutions to the numerical problems they made two different methods.
Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).
Hence both options are the same and true.
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Write another division problem that has a quotient of 3 and a remainder of 28.
Division problem with quotient of 3 and a remainder of 28 are-
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.Explain the term quotient of the division?The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient.In this example, the number being divided (15) is known as the dividend, as well as the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 ÷ 3 = 5 is a correct equation even if you change the quotient and divisor. 15 ÷ 5 = 3.The given data is-
quotient=3remainder=28To estimate:
division problem?
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.To know more about the quotient of the division, here
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Through C construct a parallel to AB.
Through A construct a parallel to BC.
Through B construct a parallel to AC.
Extend these lines to form a new triangle.
What relationship exists between the
two triangles?
A
C
B
Answer:
new triangle is similar to and 2 times the size of the original
Step-by-step explanation:
You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.
ConstructionThe attachment shows the described construction.
RelationshipThe sides of the original triangle are midsegments of the new triangle, so the new triangle is ...
scaled up by a factor of 2 (has 4 times the area)similar to the originalrotated 180° about the common centroid of the two trianglesYou are given the statement: Vertical angles are equal in measure.
A. Rewrite the statement as an if-then statement.
B. Write the converse of the implication.
The if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
What is the Converse Statement?
That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.
We have given the statement:
Vertical angles are equal in measure.
A). Rewrite the statement as an if-then statement.
If angles are vertical angles then their measure is equal.
B). Write the converse of the implication
If the measure of angles is equal then they are vertical angles.
Hence, the if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
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what is 309x317/9-4+7/8x3
[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]
3. Solve the main denomonator.[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]
4. Solve the secondary denominator.[tex]\frac{(\frac{309*317}{12})}{24}[/tex]
5. Solve the secondary numerator.[tex]\frac{(\frac{97953}{12})}{24}[/tex]
6. Solve the main numerator.[tex]\frac{(8162.75)}{24}[/tex]
7. Simplify the fraction.[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Can anyone help me ASAP?
Answer:
Equation 1 - x + 4y = 12
Equation 2 - 2x + 4x = 16
Cost of 1 Cheeseburger - $4
Cost of 1 Taco - $2
Step-by-step explanation:
Cheeseburger(x) and Taco(y)
x + 4y = 12 and 2x + 4y = 16
x = - 4y + 12
2(- 4y + 12) + 4y = 16
- 8y + 24 + 4y = 16
- 4y = - 8
y = 2
x + 4(2) = 12
x + 8 = 12
x = 4
A company has computed a seasonal index for its quarterly sales. Which of the following statements is not correct?
Multiple Choice
The sum of the four quarterly seasonal index numbers is 4.
The index for any quarter must be between 0 and 2.
The average index is 1.
An index of 0.75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
An index of 1.10 indicates sales 10% above the norm.
The option b "The index for any quarter must be between 0 and 2" is correct.
In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.
For its quarterly sales, the corporation has created a seasonal indicator.
Consequently, it is correct that the four quarterly seasonal index figures add up to 4.
True, the average index is 1.
In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.
Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.
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Can someone please solve this its on computer and im only good on paper
By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)
How to Solve a System of Equations by Graphing?The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.
To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.
Given the system of equations,
y = 5x + 2
y = x - 2
The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.
The point of intersection is at (-1, -3). Therefore, the solution is:
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11. A triangle has a base length of 3.9 cm and a height of 9 cm. Which dimensions could
be the measurements of a similar triangle?
The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm
How to Identify a similar triangle?Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.
Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.
Thus, this means that a similar triangle will have same ratio of side lengths. Thus;
If new height is h and new base is b, then we have;
9/h = 3.9/b
Thus,
h/b = 9/3.9
If we multiply the right side top and bottom by 2, then we have;
h/b = 18/7.8
18 and 7.8 cm could be similar dimensions.
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a line passes through the point (-6,3) and has a slope of 3/2
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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The Picture and Sound electronics store has hired Brennan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. He turns the crank 15 times to lift a box 15 feet. He turns the crank 45 times to lift a box 45 feet.
In this relationship, x represents the number of times Brennan turns the crank to lift a box, and y represents the height the box has been lifted (in feet).
Graph two points for this relationship and the line passing through them.
The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.
What is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.
The number of times Brennan turns the crank = x
The height to which the box is lifted = y
The points on the graph are; (15, 15), and (45, 45)
The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship
A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)
Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel
The relationship between the variables x and y is; y = x
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Find the value of each of these quantities a) P(6,3) c) P(8,1) e) P(8,8) b) P(6,5) d) P(8,5) f) P(10,9)
The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.
The formula to calculate the permutation is , P = n! / ( n - r )!. Using this formula we get the result as,
P(6,3) = 6! / (6−3)!
= 6! / 3!
= 120
P(8,1) = 8! / (8 - 1)!
= 8! / 7!
= 8
P(6,5) = 6! / (6-5)!
6! / 1!
720
Similarly ,
P(8,8)= 40320
P(8,5) = 6720
P(10,9) = 3628800
A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.
For example, the permutation of set A=1,6 is 2, as in 1,6,1.
There are no alternative ways to arrange the items in set A, as you can see.
In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination
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Which property justifies the statement below? X(y+5)=xy+5x
