Answer:
6
Step-by-step explanation:
help me pleasee will mark brilliantep
Since
AB/DC = AC /CE - Given; and
AB || CD - Given
Where BCA = DEC = 90°
Therefore, ΔABC ~ ΔCDE - Side-Side-Similarity.
What does the theorem of Side-Side- Similarity state?The theorem of Side-Side-Similarity (SSS) states that if in two triangles, the lengths of corresponding sides are proportional, then the triangles are similar. More specifically, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.
This theorem is one of the three criteria for similarity of triangles, the other two being Angle-Angle (AA) similarity and Side-Angle-Side (SAS) similarity.
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Maths, please help, I'm very stuck.
The scale of the map is 1:2, the distance from Averton to Charlbrough is 12 kilometers, and the distance in the map is 6.25 cm.
What is the scale on the map?We know that 25 kilometers are represented in the map using only 12.5 centimeters. Now, let's simplify this:
25 kilometers / 12. 5 cm = 2
This can be expressed as a scale of 1:2 in which each centimeter represents 2 kilometers.
What is the distance between Averton to Charlbrough?We know the distance on the map is 6 cm, let's now convert this to kilometers:
6cm x 2 = 12 kilometers
What is the distance on the map?We know the distance is 12.5, using this information let's find out the distance on the map.
12.5/ 2 =6.25 cm.
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Find m (photo below)
Applying the linear pair theorem, the measures of the angles in degrees are:
m<ABD = 112°; m<DBC = 68°
What is the Linear Pair Theorem?The Linear Pair Theorem, also known as the Linear Pair Postulate, is a basic postulate in geometry that describes the relationship between two adjacent angles that form a straight line.
According to the Linear Pair Theorem, if two angles are adjacent and form a straight line, then they are supplementary. In other words, their measures add up to 180 degrees.
Therefore, according to the linear pair theorem, we have:
m<ABD + m<DBC = 180°
Substitute:
7x + 196 + 9x + 176 = 180
16x + 372 = 180
16x = 180 - 372
16x = -192
x = -192/16
x = -12
m<ABD = 7x + 196 = 7(-12) + 196 = 112°
m<DBC = 9x + 176 = 9(-12) + 176 = 68°
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Do the values in the table represent a linear function? if so what is the function rule?
The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.
To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.
Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.
To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:
slope = change in output / change in input = 3/1 = 3
Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:
y = mx + b
6 = 3(0) + b
b = 6
Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:
y = 3x + 6
This means that for any input value x, the output value y is equal to three times x plus six.
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What percentage of males prefer football? *
Male
Female
Total
15%
48%
20%
13%
Baseball Basketball Football
13
23
36
15
16
31
20
13
33
Total
48
52
100
The percentage of males who prefer football to baseball and basketball is 20%.
What is the percentage?The percentage refers to the quotient or ratios between two values or quantities.
In this situation, the percentage of males who prefer football to baseball or basketball is expressed as the number of football fans over the total number of the three sports fans.
To compute the percentage, the quotient is multiplied by 100.
Baseball Basketball Football Total
Male 13 15 20 48
Female 23 16 13 52
Total 36 31 33 100
Percentage of males who prefer football = 20% (20/100 x 100)
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Muffy ordered 3 muffins and 2 lattes for $7. Sammy ordered 4 muffins and a latte for $6. create a system of equations.
Step-by-step explanation:
I added a photo of my solution
Answer:
3m+2L = 7
4m + L = 6
Step-by-step explanation:
Let m = cost of the muffins
Let L = cost of the lattes
3m+2L = 7
4m + L = 6
To solve
Multiply the second equation by -2 and add them together.
3m+2L = 7
-8m + -2L = -12
-------------------------
-5m = -5
Divide by -5
-5m/-5 = -5/-5
m = 1
Then
4(1) +L = 6
L = 6-4
L =2
The solution is
muffins cost 1 dollar and lattes cost 2 dollars.
2. Indicate whether each system of equations has no solution, one solution, or
an infinite number of solutions by placing an X in the appropriate column.
2x-3y=3 and -4x+6y= 6
3x-2y=3 and x + 2y = 5
-8x +12y = -12 and 2x-3y = 3
y = -x + 2 and y=3x-2
No
Solution
One
Solution
Infinite
Solutions
The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions
2·x - 3·y = 3 and -4·x + 6·y = 6
3·x - 2·y = 3 and x + 2·y = 5
-8·x + 12·y = -12 and 2·x - 3·y = 3
y = -x + 2 and y = 3·x - 2
What is a system of equations?A system of equations is a set of two or more equations that are formed by the same variable.
Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions
1. 2·x - 3·y = 3 and -4·x + 6·y = 6
Multiplying the first equation by 2, we get; 4·x - 6·y = 6.
Adding the above equation to the second equation,we get;
4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12
0 = 12 (False)
Therefore, the system has no solution
2. 3·x - 2·y = 3 and x + 2·y = 5
Adding the two equations, we get;
3·x - 2·y + (x + 2·y) = 3 + 5 = 8
4·x = 8
x = 8/4 = 2
Substituting x = 2 into the second equation, we get;
x + 2·y = 5
2 + 2·y = 5
2·y = 5 - 2 = 3
y = 3/2 = 1.5
y = 1.5
Therefore, the system has one solution
3. -8·x + 12·y = -12 and 2·x - 3·y = 3
Multiplying the second equation by 4, we get; 8·x - 12·y = 12
Adding the product of the second equation and 4 to the first equation we get;
8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0
0 = 0
Therefore, the system has infinite number of solutions
4. y = -x + 2 and y = 3·x - 2
Substituting y = -x + 2 into the second equation, we get;
-x + 2 = 3·x - 2
3·x - 2 = -x + 2
3·x + x = 2 + 2 = 4
4·x = 4
x = 4/4 = 1
x = 1
y = -x + 2
y = -1 + 2 = 1
y = 1
Therefore, the system has one solution.
Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.
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which of these numbers of different license plates can be determined using only the product rule (without the use of the sum rule or some other rule)? (select all that apply.)
There can be 78,364,164,096 different license plates created if there are 7 numbers or letters on the plate, determined using the product rule.
We can use the product rule to determine the number of different license plates that can be created if there are 7 numbers or letters on the plate.
Assuming that each position on the license plate can be filled with any number or letter, we can use the multiplication principle to find the total number of possibilities. For each position, there are 26 letters and 10 digits to choose from (assuming the use of the English alphabet), so there are 36 choices for each position.
Therefore, the total number of different license plates that can be created is:
36 x 36 x 36 x 36 x 36 x 36 x 36 = 36^7
This simplifies to:
78,364,164,096
So there are 78,364,164,096 different license plates that can be created if there are 7 numbers or letters on the plate.
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--The given question is incomplete, the complete question is given
" which of these numbers of different license plates can be determined if there are 7 numbers or letters on the plate? using only the product rule (without the use of the sum rule or some other rule)?
meghan, a researcher at um, conducted a similar survey among michigan residents. she used a random sample of the same size as the study conducted by the pew research center and obtained the same value for the sample proportion. gloria is concerned that the computation of the margin of error for a confidence interval for the population proportion will be affected by the fact that the population size for all michigan residents is much smaller than that for all us adults. do you agree with gloria's concern?
Yes, Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.
Sample
A subset of the population is known as a sample. A sample is a smaller group of individuals or things chosen from the population.
Error
The distinction between the estimated value of a population parameter and the true, but unknown, value of that parameter is referred to as an error. Sampling error is the difference between the sample statistic and the population parameter. Inference is less accurate if the sample is too small or if the sample is biased, and the resulting sample statistics may differ from the actual population parameters.
Hence, from the above, we can conclude that yes the Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.
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which transformation carries the rhombus below onto itself?
1. a rotation of 180 clockwise about (-2,-2)
2. a rotation of 90 counterclockwise about (-2,-2)
3. a reflection over the line y=x+10
4. a reflection over the line y=-x-6
Therefore, the answer is option 4: a reflection over the line y=-x-6.
What is transformation?In mathematics, a transformation is a process that changes the position, size, or shape of a geometric object in some way. Transformations are often used in geometry and other branches of mathematics to study the properties of shapes and their relationships to each other.
Here,
To determine which transformation carries the rhombus onto itself, we need to identify the symmetries of the rhombus. A rhombus has two types of symmetry: rotational symmetry and reflectional symmetry.
Option 1: a rotation of 180 degrees clockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 180 degrees clockwise about the point (-2,-2). Since the rhombus has rotational symmetry of order 2 (i.e., a rotation of 180 degrees carries the rhombus onto itself), this transformation carries the rhombus onto itself.
Option 2: a rotation of 90 degrees counterclockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 90 degrees counterclockwise about the point (-2,-2). Since the rhombus does not have rotational symmetry of order 4 (i.e., a rotation of 90 degrees does not carry the rhombus onto itself), this transformation does not carry the rhombus onto itself.
Option 3: a reflection over the line y=x+10
This transformation reflects each point of the rhombus over the line y=x+10. Since the rhombus does not have reflectional symmetry over this line, this transformation does not carry the rhombus onto itself.
Option 4: a reflection over the line y=-x-6
This transformation reflects each point of the rhombus over the line y=-x-6. Since the rhombus has reflectional symmetry over this line, this transformation carries the rhombus onto itself.
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11y + 3(2y - 4) slove
Answer:
Step-by-step explanation:
17y-12
11y+3(2y-4)
11y+6y-12
17y-12
I hope this helps!
A diver descends to a depth of –25. 6 feet relative to sea level. How many feet must the diver ascend to reach sea level? 0. 6 feet 25 feet 25. 6 feet 256 feet
A height of 25.6 feet above the earth is required of the diver. So , the correct choice is C ) 25.6.
Assumed: A diver descends 25.6 feet below sea level.
He would be at sea level at that point, therefore the distance would be 0.
As a result, he must ascend 25.6 feet from sea level to reach 0 feet.
In order to descend to the sea level, the diver must ascend 25.6 feet.
As a result, in order to return to sea level from the diver's current depth of 25.6 feet below it, they must climb 25.6 feet. 25.6 feet is the correct answer.
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Can someone please help me
A statement about the model that is true include the following: A. the number of customers visiting the bodega decrease by 25 for every inch of rainfall.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the y-intercept or initial number.Based on the information provided above, an equation that models the situation is given by;
y = 90 + (-25)x
y = 90 - 25x
By comparison of the two equations, we have:
mx = -25x
Slope, m = -25.
In conclusion, the rate of change is -25 customers per inch of rain.
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8x-4x+2y-4z+3z
I just need the answer
let f(x)=3|x-7|+11. write a function g whose graph is a vertical shrink of the graph of f by a factor of 1/2
c) the united states has a population of about 320 million. if our homicide deaths were proportional to that of honduras, how many deaths would we expect in the united states due to homicides? round to the nearest person.
The United States has a population of about 320 million, so if homicides were proportional to Honduras' rate of homicide, we would expect about 12,800 deaths due to homicides in the United States.
This is calculated by taking the population of the United States (320 million) and multiplying it by the Honduras' homicide rate of 40 per 100,000 people.
To calculate this, we first need to find Honduras' homicide rate. The World Bank has this information, which states that the rate is 40 per 100,000 people. We then need to take the population of the United States (320 million) and multiply it by the rate.
This equals 128 million homicides per 100,000 people in the United States. This comes out to 12,800 deaths due to homicides in the United States. Round this to the nearest person, and you get 12,800.
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I’m stuck on this question
[tex]\cos( 50^o )=\cfrac{\stackrel{adjacent}{MN}}{\underset{hypotenuse}{MO}}[/tex]
keep in mind that the opposite side is the side "facing off" the angle, and the adjacent is the one "not" facing it off.
Need HELP ASAP!!!! RIGHT NOW!!!! THIS INSTANT!!!!
The value of a brand new car is $10,000 and the value depreciates 18% every year. Write a function to represent the value of the car after t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.
The function representing the value of car is 10000 (1 - 0.045)[tex]^{(4t)}[/tex]. The percentage rate of change per quarter is 0.68%. The solution has been obtained by using the substitution method.
What is the substitution method?
The substitution approach is a widely used method in algebra for solving simultaneous linear equations. The name of the method implies that the value of one variable from one equation is changed in the second equation.
We are given that the value of car depreciates 18% every year.
Let f(t) represent the car's worth after t years.
So, we get the function as:
⇒ f(t) = 10000 (1 - 0.18/4)[tex]^{(4t)}[/tex]
⇒ f(t) = 10000 (1 - 0.045)[tex]^{(4t)}[/tex]
Now, the percentage rate of change per quarter is:
⇒ r = [tex](1-q)^{4}[/tex] - 1
Here, q = 0.045
On substituting the value, we get
⇒ r = [tex](1-0.045)^{4}[/tex] - 1
⇒ r = -0.68%
Hence, the required solutions have been obtained.
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The length of a rectangle is 7 centimeters less than three times its width. Its area is 40 square centimeters. Find the dimensions of the rectangle. Use the formula, areaequals length times width.
The length and the width of the rectangle are 1cm and 8/3cm
How to determine the dimensionsThe formula that is used to calculate the area of a rectangle is expressed with the equation;
A = lw
Given that the parameters are;
l is the length of the rectangle.w is the width of the rectangle.A is the area of the rectangle.From the information given, we have that;
Length = 3w - 7
Substitute the values, we have;
40 = (3w - 7)w
expand the bracket
40 = 3w² - 7w
3w² - 7w - 40 = 0
3w² + 15w - 8w - 40 = 0
3w(w + 5) - 8(w + 5) = 0
w = 8/3 or - 5
Length = 3(8/3) - 7 = 1
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The relative frequency for the event "spin a 3" is __?
Answer:0.04
Step-by-step explanation:
Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars. Rena correctly writes another expression, 0.25d , that will also find the sale price of the game if the original price is d dollars. Drag each description to explain each part of both expressions.
In 1st part expression there is a subtraction of 75% of 0.75d from orignal price and in 2nd expression the discount of 75% of the orignal price.
What do you mean by an expression?In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, −, ×, ÷, etc.) that represent a quantity or a mathematical operation.
Expressions can be simple or complex, and they can involve variables, constants, and functions. Expressions can be evaluated or simplified to obtain a numerical or symbolic result.
d: This represents the original price of the video game in dollars.
0.75d: This represents the price of the video game after the 75% discount has been applied. It is equivalent to subtracting 75% of the original price (0.75 times d) from the original price (d).
0.25d: This represents the amount of the original price that is discounted by 75%. It is equivalent to subtracting the sale price (d - 0.75d) from the original price (d), since the discount is 75% or 0.75 of the original price (d).
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please solve this, thankyou
Answer:
probability of getting a red ball= 6/11
Step-by-step explanation:
we know, to find a probability of a event
1st we have to get the total number of events that can occur,i.e
6+4=11
and
the total probability of getting a red ball is 6/11
which is the required answer..
Write an equation that describes the relationships between h and t.
simultaneous equation x=5, y=1
The answer to the given problem is x = 3 and y = 1.
Define simultaneous equationSimultaneous equations are a set of equations with multiple variables that must be solved at the same time. In other words, they are equations that have more than one unknown value, and their solutions must satisfy all the equations in the system. These equations are used to model many real-world situations, such as business and engineering problems.
Given equation;
x + y = 4 ...................... (1)
2x - 5y = 1 ..................... (2)
Multiplying by 5 equation (1) we get,
5(x + y = 4)
5x + 5y = 20 ................. (3)
Adding equation (2) and (3) we get,
2x - 5y = 1
5x + 5y = 20
7x = 21
x = 21/7
x = 3
Putting x=3 in equation(2), we get
2x - 5y = 1
2(3) - 5y = 1
6 -5y =-5y = 1 - 6
-5y = -5
y = -5/-5
y = 1
As a result, the equation's answer is x = 3 and y = 1.
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The complete question is:
x+ y = 4 ; 2x - 5y = 1 solve by simultaneous equation
Question 5(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric
Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.
What is the range?
A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
Here, we have
Given: A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks for every unit up to 14.
We have to determine which measure of variability should be used for both sets of data to determine the location with the most consistent temperature.
We concluded that Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.
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Solve this system. -3x-y=10, 3x+y=-8 Somone answer this ASAP i need to turn in tonight.
Thus, the system of equation have no solution, solved by the elimination method.
Explain about the elimination method:To create an equation from one variable using the elimination approach, you can either add as well as subtract the equations.
To eliminate a variable, add the equations when the coefficients from one variable are in opposition, and subtract the equations when the coefficients from one variable are in equality.
Given system of equations are-
-3x - y = 10 ...eq 1
3x + y = -8 ... eq 2
Add both eq.
-3x - y + 3x + y = 10 - 8
0 = 2
As both value of x and y are getting cancelled.
But, 0 ≠ 2
Thus, the system of equation have no solution, solved by the elimination method.
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Let Y1 and Y2 have joint pdf
f(y1,y2)=3y1
, if 0≤y2≤y1≤1
0, otherwise.
a) Find the marginal density function for Y2.
b) For what values of y2 is the conditional density f(y1|y2)
defined?
a. The marginal density function for Y2 is fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
b. For y2 ≤ y1 ≤ 10 of y2 is the conditional density f(y1|y2) is defined
(a) To find the marginal density function for Y2, we integrate the joint pdf over all possible values of Y1:
fY2(y2) = ∫fY1,Y2(y1,y2) dy1, where the integral is taken over the range where 0 ≤ y2 ≤ y1 ≤ 10, otherwise 0.
fY2(y2) = ∫₀¹⁰3y1 dy1 = 1.5y² |₀y2 = 1.5y2², where 0 ≤ y2 ≤ 10.
So the marginal density function for Y2 is:
fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
(b) The conditional density f(y1|y2) is defined as:
f(y1|y2) = fY1,Y2(y1,y2) / fY2(y2), where fY2(y2) > 0.
So the conditional density is defined for all y1 such that 0 ≤ y2 ≤ y1 ≤ 10 and 0 ≤ y2 ≤ 10, i.e.,
y2 ≤ y1 ≤ 10.
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Geometry!! Please answer
The surface area of this rectangular prism is equal to 158 ft².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;
SA = 2(8 × 3 + 5 × 8 + 5 × 3)
SA = 2(24 + 40 + 15)
SA = 2(79)
SA = 158 ft².
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Dylan invested some money in his bank. He agreed a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period the value of his investment increased by £72. Work out the value of Dylan's initial investment.
Dylan initial investment was £1200
Interest are of two types :- 1. Simple interest
2.Compound interest
Here Dylan has invested on yearly terms therefore , We need to need to calculate the simple interest here
Given ,
Principal = ?
Interest= £72
Time = 2 years
rate = 3%
Formulae for simple interest is=( Principal * (Rate/100) *Time)
Therefore
72 = (Principal *(3/100) *2)
72 = ( Principal* 0.06)
Principal= 72/0.06
Principal= £1200
Therefore the initial investment was £1200 by dylan
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Therefore, Dylan's initial investment was £1200.
What is simple interest?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested that is added to the principal at regular intervals, usually monthly, quarterly or annually. The interest rate remains constant throughout the loan or investment term, and the interest earned or paid is calculated solely on the initial principal amount. Simple interest is commonly used for short-term loans or investments, and the formula for calculating it is straightforward:
by the question.
we can start by using the formula for simple interest:
Simple interest = Principal x Rate x Time
Where the Principal is the initial investment, the Rate is the annual interest rate, and the Time is the number of years.
We know that the Rate is 3% per annum and the Time is 2 years, so we can write:
Simple interest = Principal x 0.03 x 2
Since we are given that the value of the investment increased by £72 at the end of the 2-year period, we can set up an equation:
Value of investment - Initial investment = Simple interest
£72 = Principal x 0.03 x 2
£72 = Principal x 0.06
Principal = £72 / 0.06
Principal = £1200
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Find the area of the kite
so we can look at this as two triangles, one on the upper part, it has a base of 5+5 and a height of 5, and another triangle on the lower part, it has a base of 5+5 and a height of 12, let's get their area and sum them up.
[tex]\stackrel{ \textit{upper part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{5})}~~ + ~~\stackrel{ \textit{lower part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{12})}\implies25+60\implies \text{\LARGE 85}[/tex]