The image of the point (3, 4) with respect to the line x = y is the point that results from reflecting (3, 4) across the line x = y.
To understand this, we first need to understand what it means for a point to be reflected across a line.
Reflection is a transformation that flips a figure across a mirror line or line of reflection. In this case, the line of reflection is x = y. When a point is reflected across a line, the image point is located on the opposite side of the line from the original point, and it is the same distance from the line as the original point.
To find the image of points (3, 4) with respect to x = y, we need to first draw a line x = y in the coordinate plane. Then, we can visualize points (3, 4) on one side of the line and their image on the other side.
When we reflect points (3, 4) across the line x = y, the coordinates of the point will be flipped. The new coordinates will be (4, 3) instead of (3, 4). So the image of the point (3, 4) with respect to x=y is (4,3)
In summary, the image of the point (3, 4) with respect to the line x = y is (4, 3), which is the point that results from reflecting (3, 4) across the line x = y by flipping the coordinates of the point.
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Evaluate each expression if a=2.5 and b=-8
-|b=2a|
3|b+6|-|a|
Answer: First=Undefined (if you had a typo, please respond and I will edit)
Second=3.5
Step-by-step explanation:
-|b=2a|
-|-8=2(2.5)|
-8=5
Undefined
3|b+6|-|a|
3|-8+6|-|2.5|
3|-2|-2.5
3*2-2.5
6-2.5
3.5
Use the information to answer the question.
There is 3/4 liter of water in a pitcher. Then, Jacob pours more water into the pitcher. Now there are 2 7/10 liters of water in the pitcher.
How many liters of water did Jacob pour into the pitcher
Jacob poured 39/20 liters of water into the pitcher to make it 2 7/10 liters
What is an equation?An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.
Let x represent the amount of water that Jacob pour into the pitcher.
There is 3/4 liter of water in a pitcher. Then, Jacob pours more water into the pitcher. Now there are 2 7/10 liters of water in the pitcher.
2 7/10 liters = 27/10 liters
The equation is given as:
x + 3/4 = 27/10
x = 39/20
Jacob poured 39/20 liters of water into the pitcher
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96.458 is between which two numbers?
Answer: 96 and 97
Step-by-step explanation:
what is interesting in chapter exponents and powers
So on solving provided question we can say that the exponent will be as follows [tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex].
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
the given exponent is
[tex]e^{x^{-2y}} = e^{x^{3}} = e^{34}[/tex]
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Linear equation with colors lines black orange green and blue
The graph of Linear equation with colors lines black, orange, green and blue is shown in figure.
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)
Given that;
Linear equation with colors lines black orange green and blue.
Now, We know that;
The graph of linear equation is always a straight line.
Hence, The graph of Linear equation with colors lines black orange green and blue is shown in figure with straight line.
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Which of the ratios below is equivalent to 1:3? Select all that apply.
A) 4:12
B) 6:18
C) 6:2
D) 8:24
E) 5:8
Answer:
A, B,D
Step-by-step explanation:
A(-2, 5), and B(2, 3), find the coordinate so that p is 4/5 of the way from A to B
The coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].
What is simplest form?When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. Use division to find the simplest form of a fraction.
Given set of points
A(-2, 5)
B(2, 3)
ratio 3:5 or r = 3/5
We will use the following formula to find the coordinate
[tex]$x=\frac{x_1+r x _2}{1+r}[/tex]
[tex]$y=\frac{y _1+r y _2}{1+r}$[/tex]
Substitute the values in the formula
[tex]$ x=\frac{-2+(3 / 5) 2}{1+3 / 5}[/tex] [tex]$y=\frac{5+(3 / 5) 3}{1+(3 / 5)}[/tex]
[tex]$x=\frac{-2+6 / 5}{5+3 / 5}[/tex] [tex]$ y=\frac{59 / 5}{5+8 / 5}$[/tex]
[tex]$x=\frac{-10+6 / 5}{8 / 5}[/tex] [tex]$ y=\frac{25+9 / 5}{8 / 5}$[/tex]
[tex]$x=\frac{-4}{8}[/tex] [tex]$y=\frac{17}{4}$[/tex]
x = -1/2 y = 3[tex]\frac{1}{4}[/tex]
Thus, the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].
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Full question:
Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3: 5. Write the answer in lowest simplified fraction if necessary.
i need help with this please hurry!!!
So on solving the provided question, we can say that fraction we have are [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex] = 14/6
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here the fraction we have are
[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]
12/3 + 12/4 + 15/2
14/6
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20.25 ➗ 0.9 standard form
The value of 20.25 ÷ 0.9 in standard form is 2.25×10¹
What is standard form?The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.
This means that writing a value in the form 35.77× 10³ is very wrong in standard form because 35.77 is less than 10. But instead we write it in the form 3.577×10⁴, now 3.577 is less than 10.
The value of 20.25÷ 0.9 = 22.5
but this is not in standard form because 22.5 is greater than 10. By putting it in standard form, we divide it by 10 and multiply it by 10 again
This means that 22.5 = 2.25×10¹
Therefore 20.25 ÷ 0.9 in standard form is 2.25 × 10¹
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What is the area of the trapezoid shown? Express your answer in simplest exact form. [asy] unitsize(1.5cm); pair a=(0,0); pair b=(1,sqrt(3)); pair c=(3,sqrt(3)); pair d=(4,0); draw(a--b--c--d--a); label("2",(a+b)/2,NW); label("2",(b+c)/2,N); label("2",(c+d)/2,NE); label("~$60^\circ$",a,NE); label("$60^\circ$~",d,NW); [/asy]
The area of the trapezium shown is 57.97 cm²
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The area for a two dimensional shape is the amount of space occupied for that shape.
The area of a trapezium is given by:
Area = (1/2)(sum opposite base) * height
For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches:
Area = (1/2)(7.9 + 10.8)(6.2) = 57.97 cm²
The area is 57.97 cm²
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What are the 5 exponents?
The 5 exponents are as Zero, Unity, Negative, Fractional and Reciprocal exponent. They are defined by the mathematical properties of the number when it is raised to a certain power.
Zero exponent is the number raised to the power of 0, it is always 1.Unity exponent is the number raised to the power of 1, it is always the number itself.Negative exponent is the number raised to a negative power, it is equal to the reciprocal of the number raised to the positive power.Fractional exponent is the number raised to a fractional power, it is equal to the nth root of the number, where n is the denominator of the fractional exponent.The reciprocal exponent is the reciprocal of the number raised to the original power.Understanding these exponents is important for solving mathematical problems, especially in algebra and calculus.
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Pls help me with this
The percent of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
f(x) = 500 (0.67)ˣ
Part A :
x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500
x = 1 ⇒ f(x) = 500 (0.67)¹ = 335
x = 2 ⇒ f(x) = 500 (0.67)² = 224.45
x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815
Part B :
Here 0.67 is the decay rate.
That is the rate of decay of the bug is 0.67.
67% of the bugs are decaying with each day.
Part C :
Percent of bugs remaining each day = 100% - 67% = 33%
Part D:
f(x) < 40
500 (0.67)ˣ < 40
(0.67)ˣ < 40 / 500
(0.67)ˣ < 0.08
Taking logarithms on both sides,
㏒ (0.67)ˣ < ㏒ 0.08
x ㏒ (0.67) < ㏒ 0.08
x (-0.1739) < (-1.0969)
Dividing doth sides by (-0.1739), the sign of inequality changes because of dividing by a negative number.
x > 6.3
Hence the percentage of the bugs eaten and remained are calculated.
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A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Step-by-step explanation:
multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.
in our case the least common multiple of 4 and 9 is 36.
so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract
36x - 54y = 90
- 36x + 8y = 28
-------------------------
0 -62y = 62
so, x is "eliminated", and we can solve for y : y = -1.
and then we can use one of the original equations to solve for x.
e.g.
9x + 2×-1 = 7
9x - 2 = 7
9x = 9
x = 1
Answer:
First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.
9(4x - 6y = 10) is equivilant to 36x - 54y = 90
-4(9x + 2y = 7) is equivilant to -36x - 8y = -28
Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:
-62y = 62 we have successfully eliminated x!
The last step will be to divide both sides by -62
-62y/-62 = 62/-62
y = -1
the time required to complete a job varies inversely as the number o people working. it took 4 hours for 7 electricians to wire a building. how long would it have taken 3 electricians to have done the job
The time taken by 3 electricians to complete the work is 9 1/3 hours.
Inverse proportionality:When one quantity's value rises relative to another's decrease or vice versa, it is said that the two are inversely proportionate.
It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.
If x and y are inversely proportionate to each other
=> x ∝ 1/y
=> xy = k [ where 'k' is proportionality constant ]
Here we have
The time required to complete a job varies inversely to the number of people working. It took 4 hours for 7 electricians to wire a building.
Let x be the time and y be the number of people
Given that the time required to complete a job varies inversely to the number of people working.
=> xy = k ---- (1) [ Since they are inversely proportional to each other ]
Given that it took 4 hours for 7 electricians to wire a building.
=> 4(7) = k
=> k = 28
Substitute k = 28 given number of electricians y = 3 in equation (1)
=> x (3) = 28
=> x = 28/3 = 9 1/3hrs
Therefore,
The time taken by 3 electricians to complete the work is 9 1/3 hours.
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please help me i dont really know it
The length of line WX in both rectangles is 10.5 ft. The right option is (D) 10.5.
What is a rectangle?A rectangle is a plane shape with fours sides, having two opposite sides equal and parallel.
To calculate the length of WX, we use the formula below.
Note: Rectangle RSTV is similar to rectanngle WXYZ. And the ratio of their corresponding Lengths are equal.
Formula:
RV/WZ = RS/WX.................. Equation 1From the question,
Given:
RV = 2 ftWZ = 5 ftRS = 4.2 ftSubstitute these values into equation 1 and solve for WX
2/5 = 4.2/WXWX = (5×4.2)/2WX = 10.5 ftHence, the length of line WX is 10.5 ft
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Boden's account has a principal of $400 and a simple interest rate of 4.4%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4 years.
How to calculate simple interest?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P represents the principal or starting amount.R represents the interest rate.A represents the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 400 × 4.4/100 × 4
S.I = 400 × 0.044 × 4
S.I = $70.4.
Next, we would calculate the future value as follows;
S.I = A - P
Future value, A = S.I + P
Future value, A = $70.4 + $400
Future value, A = $470.4.
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An Internet service provider charges $18 per month plus an initial set up fee a customer paid a total of $81 after two months of service how much would it cost to customer after seven months of service
The cost to customer after seven months of service is equal to $171.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.Next, we would set up or write an equation that shows the relationship between the months of service and the total charges as follows;
y - 81 = 18(x - 2)
By making "y" the subject of formula, we have the following:
y = 18x - 36 + 81
y = 18x + 45
After seven (7) months of service, the cost is given by:
y = 18(7) + 45
y = $171.
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I need help, answer quick and pls explain
The LCM of the numbers 1 - x² and (x - 1)³ is (1 - x²)(x - 1)
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The least common multiple (LCM) of a set of numbers is the smallest number that can be divisible by the set of numbers
Given the numbers:
1 - x² and (x - 1)³
(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)
(x - 1)³ = (x - 1)(x - 1)(x - 1)
The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)
The LCM is (1 - x²)(x - 1)
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5x ( 2x^2 - 3x ) + 2x^3 - x^2
Answer:
[tex]12x^3-16x^2[/tex]
Step-by-step explanation:
[tex]10x^3-15x^2+2x^3-x^2=12x^3-16x^2[/tex]
The table gives the annual global plastic production over time, in years, since 1960.
Fit an exponential model to this data.
The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____
correlation between the model and the data, this prediction (4) _____.
Answer options:
1-
increased by 4.9 metric tons
decreased by 4.9 metric tons
increased by 4.9%
decreased by 4.9%
2-
40
60
70
3-
moderate
strong
weak
4-
is unreliable
can be accepted with confidence
The exponential model indicates that plastic production has increased by 4.9% per year.
Fit an exponential model to this data
The exponential model indicates that plastic production has increased by 4.9% per year.The model predicts that plastic production 15 years after 1960 was closest to 70 million metric tons.Because the correlation coefficient indicates strong correlation between the model and the data,this prediction can be accepted with confidence.The exponential model is a powerful tool for predicting future trends in plastic production, and it indicates that plastic production has been increasing at an annual rate of 4.9%.This is an important insight, as it can help us to anticipate the future of the industry.With this information, we can estimate that plastic production 15 years after 1960 was likely to be around 70 million metric tons.The strength of this prediction is supported by the correlation coefficient, which suggests a strong correlation between the model and the data.This suggests that the model is a good predictor of future plastic production, and that the prediction of 70 million metric tons is reliable.To learn more about the annual global plastic production over time refer to:
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PLS HELLP!!!! Cate has 2 cups of rice She divides it into 1/8cups how many servings of rice does she have?
Number of servings Cate can have is given by the equation A = 16 servings
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of servings be represented as A
Now , the equation will be
The number of cups of rice Cate has = 2 cups
The number of cups of servings Cate divides = 1/8 cups
So ,
The number of servings A = number of cups of rice Cate has / number of cups of servings Cate divides
Substituting the values in the equation , we get
The number of servings A = 2 / ( 1/8 )
On simplifying the equation , we get
The number of servings A = 2 x 8
The number of servings A = 16 servings
Therefore , the value of A is 16 servings
Hence , the number of servings is 16 servings
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What is the value of x in the equation 1.5 x 4 )- 3?
The value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.
The BODMAS rule is a rule used to simplify a mathematical equation. BODMAS itself is an abbreviation of the Bracket, Order, Division, Multiplication, Addition, and Subtraction. This rule indicates the sequence in which a mathematical equation should be solved.
As we want to find the value of x, firstly we have to simplify the equation by applying the BODMAS rule to the given equation:
1.5 (x + 4) - 3 = 4.5 (x - 2)
Since there's no Bracket, Order dan Division part that can be solved, so the first step is applying the Multiply part:
1.5x + 6 - 3 = 4.5x - 9
Then we apply the addition and subtraction part:
1.5x - 4.5x = - 9 - 6 + 3
- 3x = - 12
x = 4
Thus, the value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.
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(4x - 8) - (3x + 10)
[tex](4x - 8) - (3x + 10)[/tex]
Distribute negative sign:
[tex]4x-8+-1(3x)+(-1)(10)[/tex]
[tex]4x-8-3x-10[/tex]
Combine Like Terms:
[tex](4x-3x)+(-8-10)[/tex]
[tex]=\fbox{x - 18}[/tex]
Answer:
[tex]x - 18[/tex]
[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]
Mariu buy computer for £915. 00 each and ell them for £2081. 00 each. What i hi total profit on the ale of 13 computer?
Mariu buy computer for £915. 00 each and ell them for £2081. 00 each. then the total profit on the ale of 13 computer is £15158.00
What is a simple definition of profit?
the excess of returns over expenditure in a transaction or series of transactions. especially : the excess of the selling price of goods over their cost. 3. : net income usually for a given period of time.
The profit on the sale of 1 computer is the difference between the selling price and the buying price.
Profit on 1 computer:
£2081.00 - £915.00 = £1166.00
The profit on 13 computers is 13 times the profit on 1 computer.
13 × £1166.00 = £15158.00
£15158.00
hence Mariu buy computer for £915. 00 each and ell them for £2081. 00 each.then the total profit on the ale of 13 computer is £15158.00
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1.5x+3=-39
Solve for x
Show work
Answer: x=-28
Step-by-step explanation:
Answer: -28
Step-by-step explanation:
1.5x+3=-39
-3 -3
1.5x=-42
__ __
1.5 1.5
x = -28
lines mean divide
Solve the equation below for x.
Answer:
x=-9ln(1/2)/[ln(4)-ln(1/2)]
Step-by-step explanation:
4^{x}=(1/2)^{x-9}
ln(4^{x})=ln((1/2)^{x-9})
xln(4)=(x-9)ln(1/2)
xln(4)=xln(1/2)-9ln(1/2)
xln(4)-xln(1/2)=-9ln(1/2)
x[ln(4)-ln(1/2)]=-9ln(1/2)
x=-9ln(1/2)/[ln(4)-ln(1/2)]
2/3 x 85 greater or equal
Answer:
2/3<85
I hope I help you in this ans and tq.
A lot measures 63.41 feet. What is the measurement in feet’s inches and fractions of an inch? Answe to the nearest 1/16
The measurement 63.42 feet after conversion is 760.92 inches.
What is conversion of measurement?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, the right conversion factor to an equivalent value must be applied. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
Here the given measurement is ,
=> 63.41 feet
To convert feet into inches we need to multiply by 12. Then
=> 63.41 × 12 = 760.92 inches.
Hence the given measurement into inches 760.92 inches.
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Ivania ue 9. 5 pint of blue paint and white paint to paint her bedroom wall one fourth of thi amount i blue paint and the ret i white paint how many pint of white paint did he ued to paint her bedroom wall
7 pints of white paint were used to paint her bedroom wall. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.
The total amount of paint used is 9.5 pints.
One fourth of 9.5 pints is 2.375 pints of blue paint.
The remaining amount of paint is 9.5 - 2.375 = 7.125 pints of white paint.
Therefore, 7 pints of white paint were used to paint her bedroom wall.
Ivania used 9.5 pints of blue and white paint to paint her bedroom wall. One fourth of this amount was blue paint, meaning 2.375 pints of blue paint were used. This leaves the remaining amount of paint as 9.5 - 2.375 = 7.125 pints of white paint. Therefore, 7 pints of white paint were used to paint her bedroom wall. This means that the majority of the paint used was white paint, with only a quarter of the paint used being blue. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.
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Given the formula for simple interest: i=Prt, answer the following.
(Remember, i=interest, P=the principal amount, r=the interest rate per year as a decimal, t=time in years)
If the interest paid was $37.50 on a principal of $1500 for 6 months, what was the interest rate?
Give a numeric answer only with the percentage rate (NOT the decimal rate). Do not include work, units, or explanation. If necessary, round your answer to the nearest hundredth.
Answer:
I= PTR/100 where P=Principal, T = Time period in years, R = Rate of interest per annum.