x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.
Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.
[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
specifying the least squares regression line is called the least squares regression equation.
Example,
Find the least squares regression line for the five-point data set
x = 2 2 6 8 10
y= 0 1 2 3 3.
compute the table,
x y x2 xy
2 0 4 0
2 1 4 2
6 2 36 12
8 3 64 24
10 3 100 30
28 9 208 68 (sum)
[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]
The regression line is y=0.34375x-0.125
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3. CONSTRUCTION
The diagram shows an
example of the Pratt truss used in bridge
construction.
Find m/1.
The angle ∠1 is 55 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that diagram shows an example of the Pratt truss used in bridge
construction.
We need to find the angle ∠1.
The given triangle is a right angle triangle which has one angle 90 degrees.
The adjacent angle to 145 degrees be angle 2.
145+∠2=180
∠2=180-145
∠2=35 degrees.
We know that the sum of three angles is 180 degrees
So ∠1+35+90=180
∠1+125=180
Subtract 125 from both sides
∠1=180-125
∠1=55
Hence, the measure ∠1 is 55 degrees.
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how many zeros in a million
Answer:
There are 6 zeros in one million.
Step-by-step explanation:
1000000 (one million)
6 zeros
Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
Which Postulate or Theorem is stated above?
Question 1 options:
Polygon Similarity Postulate
Polygon Congruence Postulate
Angle-Angle Similarity Postulate
Side-Side-Side Similarity Theorem
Side-Angle-Side Similarity Theorem
Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
The statement above is the Angle-Angle Similarity Postulate, which states that two polygons are similar if and only if they have two corresponding angles that are congruent.
Hence, Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
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Answer:
Angle-Angle Similarity Postulate
Step-by-step explanation:
9tailsminato9.
Wayne earns 5.3% simple interest for 5 years on $3000. How much interest does he earn on the account? I=prt
*
1 point
$883.86
$795
$3,883.86
$1,795
Answer: I would say it’s D. $1,795
Step-by-step explanation: why not pick D….
Hope this helps^^
The simple interest earned on $3000 after 5 years at 5.3% rate of interest is $795. The correct option is C .
Given,
Principal amount = $3000
Rate of interest = 5.3%
Time = 5 years
Now,
Simple interest = Principal × ROI ×Time/100
Substitute the values ,
Simple interest = 3000 * 5.3 * 5/ 100
Simple interest = 79500/100
Simple interest = $795
Total amount after 5 years = $3000 + $795
= $3795
Hence simple interest earned on $3000 at ROI of 5.3% after 5 years will be $795 .
Therefore option C is correct.
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Please work the problem
Answer:
6x-7=3x-29
6x-3x=-29+7
3x=-23
x=-23/3
6x-7=8y+17
6(-23/3)-7=8y+17
-46-7=8y+17
8y+17+53=0
y=70/8
Y=8.75
ANS!!
In the figure, the person is 5 ft tall and his shadow is 4 ft long. The tree's shadow is 22 ft long.
What is the height of the tree? Show all your work.
Answer: The height of the tree is approximately 44 ft.
Step-by-step explanation: Step 1: Calculate the ratio of the person's height to the length of their shadow.
Person's Height: 5 ft
Length of Shadow: 4 ft
Ratio: 5 ft/4 ft = 1.25
Step 2: Use the ratio to calculate the length of the tree's shadow.
Length of Tree's Shadow: 22 ft
Ratio: 1.25
Calculation: 22 ft/1.25 = 17.6 ft
Step 3: Multiply the length of the tree's shadow by the ratio to calculate the tree's height.
Length of Tree's Shadow: 17.6 ft
Ratio: 1.25
Calculation: 17.6 ft x 1.25 = 22 ft
Answer: The height of the tree is approximately 44 ft.
in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC. Show that BF = CE
BF=CE in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given E and F are mid point of equal sides AB and AC of triangle ABC
In ΔABF and ΔACE
AB=AC (given )
∠A=∠A (common angle )
The side FA is equal to EA
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent
∴ΔABF≅ΔACE (SAS rule)
∴BF=CF ( Corresponding parts of Congruent triangles.)
Hence, in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC then BF=CE.
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There are 400 eighth graders at Wilson Middle SchoolIn the class president election, 296 students voted for Luke, 60 students voted Alice, and 44 students voted for Chris.who voted for luke
Answer: In the class president election at Wilson Middle School, 296 students voted for Luke.
Step-by-step explanation:
A rectangle has a length of 19 inches and a
vidth of 15 inches. What is the perimeter
of the rectangle?
The perimeter is
inches.
Answer:
Step-by-step explanation:
So when solving for the perimeter you need to add up all the sides. So 15 + 15 = 30 and 19 + 19 = 38. So 38 + 30 = 68 inches. So there is your answer. 68 inches is the perimeter.
Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister that she has to pay back before she can start saving.
This relationship can be shown by a linear function. Below is a table showing how many hours Yvette has worked (input), and how much money she's saved (output).
Hours Worked (x) Amount Saved (y)
0 -$25
4 $14
8 $53
12 $92
16 $131
Which of the following statements are true regarding the graph of this linear function? Select all that apply.
Group of answer choices:
A. The slope of the line, 25, is the amount of money she makes per hour of work.
B. The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours.
C. The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours.
D. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
E. The slope of the lines, 9.75, is the amount of money she makes per hour of work.
The slope of the line is 9.75 and the y-intercept is -25.
What is a linear function?
Two distinct but related concepts are referred to by the phrase "linear function": A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
Here, we have
Given: Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister which she has to pay back before she can start saving.
Let the linear function that models the given situation be y = ax + b. Here, a and b are constants. We can use this information to find the values of a and b.
We put x = 0 and y = -25 into y = ax + b
b = -25
Substitute the value of b into y = ax + b
y = ax -25...(1)
Now we put x = 4 and y = 14 in equation(1) and we get
14 = 4a - 25
4a = 39
a = 9.75
Substitute the value of a in equation (1):
y = 9.75x - 25
Compare the above function with the slope-intercept form of a line y = mx + c
m = 9.75, c = -25
Hence, the slope of the line is 9.75 and the y-intercept is -25.
A. From the previous calculations, it is clear that the slope of the line is 9.75. Hence, the first statement is not true.
B. From the given table, it is known that person Y had started working with -25 dollars. Clearly, 9.75 is the slope of the line, but it does not represent the initial amount that person Y had at x = 0. Hence, the second statement is not true.
C. From the previous calculations, it is clear that the y-intercept is -25, not 0. Hence, the third statement is not true.
D. From the previous calculations and the given table, it is clear that the y-intercept is -25, and it does represent the initial amount that person Y had at x = 0. Note that the y-intercept is negative as the person has borrowed 25 dollars from her sister. Hence, the fourth statement is true.
E. From the previous calculations, it is clear that the slope of the line is 9.75. It is known that the slope of a line represents the rate of change in the value of y with respect to x. So, it can be concluded that 9.75 represents the amount that person Y earns per hour. Hence, the fifth statement is true.
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How is matrix multiplication done in MATLAB?
The " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles.
So the " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles. In MATLAB, the standard syntax for multiplying matrices is:
When the dimensions of A and B satisfy the matrix multiplication rule, the css copy code C = A * B can be used. Particularly, the number of rows in matrix B and the number of columns in matrix A must match.
The resulting matrix C will be the same size in terms of both rows and columns as matrix A and matrix B. Here is an illustration of how matrix multiplication functions in MATLAB:
A = [1 2; 3 4];% Define matrix A B = [5 6; 7 8];% specify matrix.
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How much warmer is 92 than 40?
The temperature measure 92 is warmer than 40 by a measure of; 52.
By how much is 92 warmer than 40?It follows from the task content that it is required to be determined, how much warmer is 92 than 40.
Since the greater temperature measure is; 92 while the lesser is 40.
It can be concluded that the temperature difference is; 92 - 40 = 52.
Ultimately, the measure 92 is 52 warmer than 40.
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In order to ride a
roller coaster at the theme park, riders
must be at least 52 inches tall. Write
an inequality to show the
safe heights for riders.
The inequality to represent the height of roller coaster is x≥52.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that. in order to ride a roller coaster at the theme park, riders must be at least 52 inches tall.
Let the height be x.
Now, x≥52
Therefore, the inequality is x≥52.
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i need help :) if any of you know how to do this I would appreciate it.
Step-by-step explanation:
So in order to find out how much he needs to sell, let's find out what the target is. We do that by working options A.
$19 for 40 hours
[tex]40 \times 19 = 760[/tex]
Now that we have 760, we know this amount is 8%. Next we setup a ratio
[tex] \frac{760}{x} = \frac{8\%}{100\%} [/tex]
We cross multiply
[tex]8x = (760)(100)[/tex]
[tex]8x = 76000[/tex]
Last but not least, we divide by 8 on both sides
[tex]x = 9500[/tex]
Find an expression that represents the difference when (-4x+4) is subtracted from (-9x-7) in simplest terms.
The required simplified expression result of (-4x+4) is subtracted from (-9x-7) is -5x -11.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression (-9x-7) - (-4x+4) can be simplified as follows:
First, we'll combine the like terms:
-9x - 7 - (-4x + 4)
Next, we'll use the distributive property to simplify the right side:
-9x - 7 - (-4x) + 4
Combining like terms on the right side:
-9x - 7 + 4x - 4
Combining the remaining terms:
-5x -11
Thus, the requried simplified expression is given as -5x-11.
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Nelson claims that when the length and the breadth of a rectangle change by +20% and -20% respectively, the area of the rectangle will remain unchanged. Do you agree? Explain your answer.
Answer: No, the area will not stay the same.
The new area is smaller than the old area.
========================================================
Explanation:
Let's look at an example.
Consider a 10 by 30 rectangle. Its area is 10*30 = 300 square units.
Now let's change the length and width.
Increase the "10" by 20% to get 10*1.20 = 12Decrease the "30" by 20% to get 30*(1-0.20) = 30*0.80 = 24The rectangle is now 12 by 24. The new area is 12*24 = 288 square units.
In summary:
old area = 300 square unitsnew area = 288 square unitsThis is one counterexample, of infinitely many, that proves the area does not stay the same. Instead, the area shrinks.
-----------------
This section will go over a more formal proof using algebra.
L = lengthW = widthold area = length*width = LW
Let's say the length increases by 20% and the width decreases by 20%.
L becomes 1.20L after the 20% increase.W becomes 0.80W after the 20% decrease (since 100%-20% = 80%)Then,
new area = (new length)*(new width)
new area = (1.20L)*(0.80W)
new area = (1.20*0.80)*(LW)
new area = 0.96*(LW)
new area = 0.96*(old area)
This shows that the new area is 96% of the old area. There has been a 4% reduction (since 100% - 96% = 4%)
Notice how 96% of 300 = 0.96*300 = 288. See the previous section above.
Tamara is buying balloons and streamers to decorate for a party. She wants to spend no more than $15 on decorations.
One package of balloons costs $4.50. Streamers are $1.50 per roll.
Tamara knows she will be buying at least 2 rolls of streamers.
Let x=
the number of packages of balloons
Let y=
the number of streamer rolls
Graph the system of inequalities and choose the region that represents the combinations of balloons and streamers that Tamara can purchase.
A graph of the system of inequalities is shown in the image attached below.
The region that represents the combinations of balloons and streamers that Tamara can purchase is the shaded region that contains the point (1, 3).
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of balloons and number of streamer rolls respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of balloons.Let the variable y represent the number of streamer rolls.Since one package of balloons costs $4.50 and streamers are $1.50 per roll, and Tamara wants to spend no more than $15 on decorations, a linear inequality to describe this situation is given by:
4.50x + 1.50y ≤ 15.
Additionally, Tamara knows she will be buying at least 2 rolls of streamers;
y ≥ 2
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HELP HELP HELP HELP HELP HELP
We would expect to see around 200 fewer accidents per year among 16-year-old drivers in your state if the proposal to increase the permit period from 6 to 12 months is implemented.
What is an estimation?Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose even when the input data is incomplete, uncertain, or unstable.
It is difficult to predict exactly how many fewer accidents would occur as a result of increasing the time a driver must hold a learner's permit from 6 to 12 months. However, there is evidence to suggest that longer permit periods can result in fewer accidents, as novice drivers have more time to gain experience under supervision before obtaining a full license.
According to research by the Insurance Institute for Highway Safety, increasing the permit period from 6 to 12 months could lead to a 20% reduction in crash rates among 16-year-old drivers.
Assuming this reduction holds true in your state, we can estimate the number of accidents that would be prevented by multiplying the current number of accidents involving 16-year-old drivers (let's assume 1,000 per year) by 20%, or 0.2. This gives us an estimated reduction of 200 accidents per year.
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Which shows how to solve the equation 3/4 X = -6 for x in one step?
To solve the equation 3/4 x = -6 for x in one step, you can multiply both sides of the equation by 4/3:
3/4 x = -6
4/3 * (3/4 x) = 4/3 * (-6)
x = 8
Determine which of the following properties are always true by dragging them to the right:
-All four sides are congruent
-Opposite sides are congruent
-Opposite sides are parallel
All four angles are congruent
-Opposite angles are congruent
Diagonals are congruent
-Diagonals bisect each other
-Diagonals intersect at a right angle
diagonals bisect interior angles
-Sum of all angles equals 360
The properties that are always true are: Opposite sides are congruent. Opposite sides are parallel. Opposite angles are congruent. Sum of all angles equals 360. Diagonals bisect each other.
What are diagonals?A diagonal in mathematics is a line that joins two solids or polygons whose vertices are not on the same edge. Generally speaking, a diagonal is a sloping or slanting line that joins the vertices of a form. The term "diagonal" refers to lateral forms with sides, edges, and corners.
The properties that are always true are:
Opposite sides are congruent.
Opposite sides are parallel.
Opposite angles are congruent.
Sum of all angles equals 360.
Diagonals bisect each other.
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Can someone please help me with this question
40 degrees Is the answer.
Hope this helps mate.
PLs give brainliest
Answer:
40
80 + (16x-4) + (9x +4) =180
x=4
BAC = (9*4+4)
BAC = 40
how do i solve -(-8q-8.7)
On solving the expression, we get -> (8q + 8.7).
What are algebraic expressions in mathematics?In mathematics, an expression or mathematical expression is a combination of terms, both constants and variables. For example -
2x + 4y + z
Given is the algebraic expression as -
- (- 8q - 8.7)
The given expression is -
- (- 8q - 8.7)
- (- 8q) - (- 8.7)
8q + 8.7
Therefore, on solving the expression {- (- 8q - 8.7)}, we get -> (8q + 8.7).
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What is the value of 205 pounds in kg
The conversion from pounds (lb) to kilograms (kg) is determined by multiplying the weight in pounds by 0.45359237. The formula to convert pounds to kilograms is kg = lb x 0.45359237.
To calculate the weight of 205 pounds in kilograms, the calculation is as follows: kg = 205 lb x 0.45359237 = 92.98 kg.Therefore, the weight of 205 pounds is equal to 92.98 kilograms. This calculation can also be used to convert any weight in pounds to its equivalent in kilograms. For example, to convert 500 pounds to kilograms, the calculation would be: kg = 500 lb x 0.45359237 = 226.79 kg.This calculation can be used to convert any weight in pounds to its equivalent in kilograms. It is important to remember that the formula must be used correctly and that all units must be consistent. It is also essential to ensure that the result is rounded to the correct number of decimal places for accuracy.
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Please help! Make you brainliest and 15 points!
Answer:
b value is 3
rise = 3 run = -2
another point could be (2,0)
Step-by-step explanation:
Solve for x. Figures are not necessarily drawn to scale.
M
X
9
N
7
Q
10.5
9
The value of x is given as follows:
x = 13.5.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The proportional relationship for the side lengths is given as follows:
9/x = 7/10.5.
Applying cross multiplication, the value of x is obtained as follows:
7x = 9 x 10.5
x = 9 x 10.5/7
x = 13.5.
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Patrice's credit card has an APR of 11%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. Her credit card record for the last 7 months is shown in the table
below.
End of
month
1
456734
Previous
balance
$0.00
$3900.00
$3857.75
$3815.96
$3774.62
$3733.73
$3693.28
New
charges
$3900.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
Payment
received
$0.00
$78.00
$77.16
$76.32
$75.49
$74.67
$73.87
Finance
charges
$0.00
$35.75
$35.36
$34.98
$34.60
$34.23
$33.86
Principal
paid
$0.00
$42.25
$41.79
$41.34
$40.89
$40.45
$40.01
New
balance
$3900.00
$3857.75
$3815.96
$3774.62
$3733.73
$3693.28
$3653.27
How much of the $3900 charge]that Patrice made during the first month has
been paid off?
The amount of the $ 3, 900 charge that Patrice has made after paying off the first month is $ 246.73.
How to find the amount ?To find the amount that Patrice has paid out of the $ 3, 900 charge to the credit card, look at the principal payments made since that day. Add them all up to get the amount paid from the charge.
The amount paid from the charge is :
= 42. 25 + 41. 79 + 41. 34 + 40. 89 + 40. 45 + 40. 01
= $ 246.73
In conclusion, out of the $ 3, 900 charge, Patrice has paid $ 246. 73.
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aiden earns 16.00 per hour if he gets a 4% raise, what will be his new hourly wage
Aiden's new hourly wage would be 16.64 per hour.
Solution:
We have been given that Aiden's hourly wage is 16.00 per hour
So, If he gets a 4% raise then his hourly wage will be,
16* (100+ 4) / 100 = 16.64
Therefore, Aiden's new hourly wage will be 16.64 per hour.
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half as big as last night’s crowd ( c = size of last night’s crowd )
verbal expression to algebraic expression
Answer: (1/2)c
To write an algebraic expression, convert parts of the verbal expression.
What is an expression?An expression is numbers or variables with operations performed between them. It does not have an equal sign.
OperationsOperations are ways we change numbers, usually to make them bigger or smaller. Examples of operations are multiplication, division, subtraction, addition, and square root.
Write an expressionThe question says: "half as big as last night’s crowd"
last night's crowd = c
'half as big' = 1/2
This is a proper fraction with the top number smaller than the bottom number. When we multiply 'c' with a proper fraction, the answer would get smaller.Therefore, we can represent the problem using the expression [tex]\frac{1}{2}c[/tex].
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How do you find the limit of a function on a calculator?
Answer:
Step-by-step explanation:
The method for finding the limit of a function on a calculator depends on the specific calculator you are using. Here are the general steps for finding the limit of a function using a graphing calculator:
Enter the function: Most graphing calculators have a function editor where you can enter the function you want to find the limit of.
Set the limit: To find the limit of the function at a particular point, you need to specify the value at which you want to find the limit. This is done by entering the limit expression, for example: limit(f(x), x, a) where f(x) is the function, x is the variable, and a is the value at which you want to find the limit.
Evaluate the limit: After entering the limit expression, you can evaluate it by pressing the "enter" or "=" button. The calculator will then display the limit of the function at the specified value.
It's important to note that a graphing calculator can only estimate the limit of a function based on the accuracy of the graph, so the result may not be exact. Additionally, some functions may have limits that cannot be evaluated using a calculator. In these cases, you may need to use analytical methods to determine the limit.
Jack spends 1 1/2times as long on his homework as Jill.
Last week, Jill spent 6 3/4hours doing homework.
How long did Jack spend doing homework?
Answer:
10.125 hours
Step-by-step explanation:
We can convert 6 3/4 hours into minutes by multiplying it by 60
this equals 405. Jill spent 405 minutes doing homework.
Jack spent 1 1/2 times as long on his homework as Jill (1 1/2 is equivalent to 1.5)
We can multiply 1.5 x 405 and get 607.5 which means Jack spent 607.5 minutes doing homework
607.5 minutes is equivalent to 10.125 hours.