So, from the question statement, we can conclude that the y and x axes are directly proportional. In order to show it in the equation form, we can write,
Y=kx (directly proportional)
y=k x
The values that are given in the question are
y = 15
and,
x = 10
Now we will put these individual values in the above relation equation of x and y,
y=k x
15=10k
k=15/10
k=1.5
So, we found the unknown factor by putting the values of the available terms. Now in order to find the new value of y, when the new values of x are given and is,
x=22
We will simply modify the relation equation,
y=k x
By putting the known terms in the above equation,
x=22, k=1.5
y=1.5 * 22
y = 33.
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Write the equation of the line through each point. Use slope-intercept form.
(-3,1) ; perpendicular to y = -(2/5)x-4
The equation of the line in slope-intercept form passing through point (-3 , 1) and perpendicular to y = -(2/5)x - 4 is y = (5/2)x + 17/2
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is perpendicular to y = -(2/5)x - 4, then their slopes are negative reciprocal of one another.
y = -(2/5)x - 4 : m = -2/5
m = 5/2
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
1 = 5/2(-3) + b
b = 17/2
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (5/2)x + 17/2
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Write a definite integral that represents the area of the region. (do not evaluate the integral.) y1 = x2 2x 3 y2 = 2x 12
The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
What is the area of the region under a curve?By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a & x = b. With the specified limits, integration can be used to calculate this area.Given:
[tex]y_1=x^2+2x+3[/tex][tex]y_2=2x+12[/tex]The points where the two intersect will be given by:
y₁ = y₂
=> x² + 2x + 3 = 2x + 12
=> x² + 3 = 12
=> x² = 9
=> x = ± 3
For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)
For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)
Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:
A₁ = [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]
For the area of the region under the second curve [tex]y_2=2x+12[/tex]:
A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]
For the required area of the region bounded by the two curves will be given by:
A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]
A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
Refer to the image for the area so bounded by the curves.
Hence, The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].
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A 95onfidence interval for population mean will be wider than a corresponding 99onfidence interval.
true/false
The statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
The statement is:
A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval.
As we know,
A 95% confidence interval is narrower than a 99% confidence interval.
Thus, the statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.
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a. Use your calculator to generate an arithmetic sequence with a common difference of -7 . How could you use a calculator to find the 6th term? The 8th term? The 20th term?
The 20th term of the arithmetic sequence is 122.
What is arithmetic sequence?nth term = a1 + d(n - 1) so here:
20th term = -30 + 8(20 - 1)
- 30 + 152
[tex]a_{20}[/tex] = 122.
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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List the domain and range of each relation. (0,4)_,(4,0),(-3,-4),(-4,-3)
Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.
What does the math term domain mean?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.What is domain and range mathematics?
A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
Domain - { 0, 4 , -3 , -4 }
Range - { 4 , 0 , -4 , -3 }
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Position and label the following triangle on the coordinate plane.
right ΔJ K L with legs JK and KL so that JK is a units long and leg KL is 4 b units long
The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Given the triangle ΔJ K L
Base = a and Perpendicular = 4b
By Pythagoras theorem,
Hyp² = Base² + Perp²
Hyp² = a² + (4b)²
LJ = √(16b² + a²).
Hence "The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²)".
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State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If p || q , then ∠2 and ∠8 are supplementary .
The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"
Given,
The statement "If p || q , then ∠2 and ∠8 are supplementary"
In the figure
p is parallel to q.
∠2 and ∠8 are lie on the opposite sides of the transversal and both are nonadjacent exterior angle
So, ∠2 and ∠8 are alternate exterior angles
If p || q , then ∠2 and ∠8 are congruent.
Hence, The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"
The complete question is :
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If p || q , then ∠2 and ∠8 are supplementary .
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What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answer:
[tex]{ \tt{change = \frac{y_{b} - y _{a} }{x _{b} - x _{a} } }} \\ \\[/tex]
xb is 4; yb is 16 [from graph (4, 16)]xa is 1; ya is 2 [from graph (1, 2)][tex]{ \tt{ change = \frac{16 - 2}{4 - 1} }} \\ \\ = { \tt{ \frac{14}{3} }} \\ \\ = 4 \frac{2}{3} [/tex]
1) -7+5= 2) 7+5 3) 7+ (-5) 4) 2+9 5) 2+(-9) adicion de numeros enteros 6) -2+9 7) 8+(-8) 8) -5+5 9) -3+(-3) 10) -5+(-5) sustraccion de numeros enteros 1) 7- (-5) 2) -7- (-5) 3) 7- (+5) 4) 2- (-9) 5) -5- (-10) 6) 5-5 7) -8- (+20) 8) -3- (-3) 9) -5- (+12) 10) 8- (+10) porfi
The results of the expressions given are:
Part 1:
1) -2
2) 12
3) 2
4) 11
5) -7
6) 7
7) 0
8) 0
9) - 6
10) - 10
Part 2:
1) 12
2) - 2
3) 2
4) 11
5) 5
6) 0
7) - 28
8) 0
9) - 17
10) -2
We solve the equations respecting the level of hierarchy:
First the operations in parentheses, then brackets and finally braces.Of the arithmetic operations, first the multiplication and divisions and then the additions and subtractions.Two like signs add the values and keep the common sign.Two unlike signs subtract the values and use the highest value sign.Part 1:
1) -7+5= -2
2) 7+5 = 12
3) 7+ (-5) = 7 - 5 = 2
4) 2+9 = 11
5) 2+(-9) = 2 - 9 = -7
6) -2+9 = 7
7) 8+(-8) = 8 - 8 = 0
8) -5+5 = 0
9) -3+(-3) = - 3 - 3 = - 6
10) -5+(-5) = - 5 - 5 = - 10
Part 2:
1) 7- (-5) = 7 + 5 = 12
2) -7- (-5) = - 7 + 5 = - 2
3) 7- (+5) = 7 - 5 = 2
4) 2- (-9) = 2 + 9 = 11
5) -5- (-10) = - 5 + 10 = 5
6) 5-5 = 0
7) -8- (+20) = - 8 - 20 = - 28
8) -3- (-3) = - 3 + 3 = 0
9) -5- (+12) = - 5 - 12 = - 17
10) 8- (+10) = 8 - 10 = -2
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Need da answer pls and thank u point will be 100
The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:
"If you love her enough to give up your world for her, don't you think she would want to do the same for you?" - People are willing to make sacrifices for the people they care about.She looked around at the stars, the moon, the trees. These were things she could count on. - Nature can be a source of courage and comfort.What are some lessons from Clare B. Dunkie's The Hollow Kingdom?One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.
Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.
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12x + 8x + 3 + x
Is it
3x+12
-9x+6 2/3
21x+3
24x
-15x+8.3
Answer:
see explanation
Step-by-step explanation:
a bit more info is needed so this may be wrong.
so first you add up the x values which is 12x+8x+x=21x
then you can see we have a problem, we dont know the x value so the answer would be 21x +3
but we can go a bit further to get an answer as 3(7x+1)
this is also known as factorisation.
so ans: 3(7x+1)
Read the problem. Identify what you need to know. Then organize the data to solve the problem.
There are 10 sophomore, 8 junior, and 9 senior members in student council. Each member is assigned to help plan one school activity during the year. There are 4 sophomores working on the field day and 6 working on the pep rally. Of the juniors, 2 are working on the field day and 5 are working on the school dance. There are 2 seniors working on the pep rally. If each activity has a total of 9 students helping to plan it, what is the probability that a randomly selected student council member is a junior or is working on the field day?
F. 1/5
G. 4/18
H. 5/9
J. 2/3
Using the combination formula, the committee can be selected in 1,211,760 ways.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Combination formula is the number of different combinations of x objects from a set of n elements.
In this problem:
There are 10 sophomore, 8 junior, and 9 senior members in student council.
They are independent, so we can just multiply them, thus;
T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!
T = 1,211,760
Hence, The committee can be selected in 1,211,760 ways.
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Write each equation in slope-intercept form. Then find the slope and y -intercept of each line. 5 x+y=4
The slope for equation y = -5x + 4 in slope - intercept form is -5 and y - intercept is (x, 4 ).
What is slope - intercept form of equation?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 slope - intercept form is y = mx + c
5x + y = 4
Now, Rearrange the equation -
y = -5x + 4
m = -5 and y intercept = (x , 4)
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Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8.2w+10) −(−8.2w+10)
The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.
How to calculate the value?It should be noted that bwsed on the information given, the expression is illustrated as:
-(-8.2w+10) −(−8.2w+10)
The signs should be taken into consideration. This will be:
-(-8.2w+10) −(−8.2w+10)
= 8.2w - 10 + 8.2w - 10
= 16.4w - 20
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Which is the equation of a line perpendicular to line AB?
Answer:
Step-by-step explanation:
y = -3x + 7
since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3
slope of line perpendicular to AB will be -3
3 3/8 - 2 1/4 ÷ 1 1/2 - in the simplest form of a fraction
Answer:
1 7/8
Step-by-step explanation:
First convert mixed fraction to improper fraction. Then do division using KCF method. Then do subtraction.KCF method.
Keep the first fractionChange division to multiplicationFlip the second fraction[tex]\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\[/tex]
[tex]\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}[/tex]
List the outliers. if there is more than one outlier, separate them by a comma. use "none", if applicable. for the data set 3 6 4 13 3 7 5 13 3 7 5 15 3 8 5 27 4 8 6 6 4 11
For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, the outliers are 3, 3, 3, 3, 15, and 27.
In statistics, outlier refers to the data point from a given data set that differs significantly from the other data points.
One way to determine the outlier in a given data set is to calculate the interquartile range.
1. Arrange the data set in ascending or descending order.
3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27
2. Divide the data set into two sets and find the median.
{3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6} , {6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27}
Q1 median = 4
Q3 median = 8
3. Solve for the IQR.
IQR = Q3 - Q1
IQR = 8 - 4
IQR = 4
4. Determine the outlier if
high outlier ≥ Q3 + (1.5 x IQR) = 8 + (1.5 x 4) = 14
high outlier ≥ 14
low outlier ≤ Q1 − (1.5 x IQR) = 4 - (1.5 x 4) = 3
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x2+6x−16 vertex form
Answer:
Hello,
Step-by-step explanation:
[tex]x^2+6x-16\\\\=x^2+2*3x+3^2-9-16\\\\=(x+3)^2-25\\[/tex]
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C = 124ft
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle as 124 ft. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
124 ft = 2 × π × (Radius of the circle)
(Radius of the circle) = 124 ft/ (2 × π)
The radius of the circle = 19.73 ft
Diameter of circle = 2 × (Radius of the circle)
= 2 × 19.73 ft
= 39.46 ft
Hence, the radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.
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17. The depth d of an aquarium tank for dolphins must be within a 5 feet margin of 50/feet deep. Write the absolute
value inequality to represent this situation.
The absolute value inequality to represent this situation is |d - 50| <= 5
How to write the absolute value inequality to represent this situation?The given parameters are
Margin = 5 feet
Depth = 50 feet
The absolute value inequality to represent this situation is
|d - Depth| <= Margin
So, we have:
|d - 50| <= 5
Hence, the absolute value inequality to represent this situation is |d - 50| <= 5
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Mt.Whitney is the highest peak in California at 14,949 feet. The city of El Centro, also in California, is 39 feet below sea level. What is the difference in elevation between in Mt. Whitney’s peak and city of El Centro?
Answer:
if the peak level is 14949 above sea level , so the difference in elevation is 14949 + 39 =14988 feet
Jim thinks that the value of a baseball card can be modeled by a decay formula and that the value will decrease at a rate of 0.2% each year. The card was originally valued at $250 in 2007.
What would Jim expect the value of the card to be in 2018?
Answer: $244.55
A = $250 ; r=0.002 t= 11 [From 2007 to 2018 , t=2018-2007]
Write each equation in slope-intercept form. -4 x+3 y=1
The slope - intercept form of the equation -4 x+3 y=1 is y = 4/3x + 1/3.
How do we find slope - intercept form?Calculate the slope (m). Keep in mind that the slope is determined by dividing the change in y by the change in x. (rise over run).Find the y-value of the y-intercept by solving (b).In the formula y=mx+b, swap out m and b with their respective values.The equation given is -
-4 x+3 y=1
As we know the slope - intercept form is -
y = mx + c
-4 x+3 y=1
Dividing the equation with 3
⇒ -4/3x + y = 1/3
Now, rearranging the equation
y = 4/3x + 1/3
where slope = 4/3
y - intercept = 1/3
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Do the equations ;x + 2 = 6
and ;(*+ 2) = 6 represent the same situation?
Explain.
The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.
How the given equations be evaluated?The given equations are presented as follows;
[tex]\frac{1}{5} \cdot x + 2 = 6...(1)[/tex]
[tex] \frac{1}{5} \cdot (x + 2) = 6...(2)[/tex]
Solving each equation for x gives;
For equation (1), x = 5×(6 - 2) = 20
x = 20
For equation (2), we have;
x = 6 × 5 - 2 = 28
x = 28
Given that the value of x in the given equations are different, the situations are different.
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PLEASE I NEED HELP QUICK EASY POINTS
Answer: f(-1) = -12
Step-by-step explanation:
To solve, we will substitute t for -1 into the function.
Given:
h(t) = (t + 7)(t - 1)
Substitute:
h(-1) = (-1 + 7)(-1 - 1)
Add and subtract:
h(-1) = (6)(-2)
Multiply:
f(-1) = -12
Consider the functions f(x)=4^x and g(x)=x-2. The function y is defined as y=f(g(x)) state the equation for y.
the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).
We are given the functions:
f ( x ) = 4ˣ
g ( x ) = x - 2
Now, we have a function y defined as:
y = f ( g ( x ) )
Now, we need to find the equation for y.
We know that:
f ( g ( x ) ) = 4⁽ ˣ⁻ ² ⁾
f ( g ( x ) ) = 4ˣ / 4²
f ( g ( x ) ) = 4ˣ / 16
Therefore, we get that, the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).
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For each function, determine whether y varies directly with x . If so, what is the constant of variation?
a. 5 x+3 y=0
-5/3 is the constant of variation where y varies directly with x.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
A DIRECT VARIATION is a mathematical relationship between two variables that can be stated mathematically by an equation in which one variable equals a constant times the other. y = kx
⇒ 5 x+3 y=0
⇒ 3y= -5x
⇒ y = -5x/3
Thus, y = -5/3 × x, here k is constant = -5/3
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Bo the baker makes the best cookies! His recipe for triple-chip cookies uses 1/2 cups of chocolate chips, 3/4 cup of butterscotch chips, and 5/8 cup of peanut butter chips. Yum! How many cups of chips does Bo use to make one batch of triple-chip cookies?
Answer:
1/2 + 3/4 + 5/8
4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups
Step-by-step explanation:
probably right dunno
This is one batch right? if so shud be right
#1: Jane has 6 feet of ribbon. If one
meter is about 3 feet, how many
meters of ribbon does Jane have?
O 12
02
O
O 1
Answer: jane has 1.5 meters of ribbon
Step-by-step explanation:
Greg bought a blanket for $36.62, a flag for $11.25, and a glove for $17.75. He paid $60 and the rest he borrowed from his friend. If Greg got $4.38 in change from the cashier, how much did he borrow from his friend to pay for all the items?
Answer:
$10
Step-by-step explanation:
Let's begin with adding all of the items Greg bought.
36.62 + 11.25 + 17.75 = 65.62
Let the money paid to the cashier be x.
Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.
Then, it must be that x=65.62+4.38
x=70
The money he borrowed from friend = 70-60=10
Therefore, the money Greg borrowed from his friend to pay for all the items is $10.
Greg borrowed $1.24 from his friend.
What is Unitary Method?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.
This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
Given:
Greg bought a blanket for $36.62,
a flag for $11.25,
and a glove for $17.75.
Total expense of the objects he brought
= 36.62+ 11.25 + 17.75
= $65.62
He paid $60 then
=65.62 - 60 = $5.62 remaining
Also, he got $4.38 in change from the cashier
= 5.62 - 4.38
= $1.24.
Hence, Greg borrowed $1.24 from his friend.
Learn more about unitary method here:
https://brainly.com/question/22056199
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