We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
3x + y = 7
-x + y = 1
Add the equations together:
2x + 2y = 8
Divide both sides by 2:
x + y = 4
Subtract the second equation from the first:
-x + y = 1
x - y = -3
Add the equations together:
2x = -2
Divide both sides by 2:
x = -1
Substitute -1 for x in the equation x + y = 4:
-1 + y = 4
Subtract -1 from both sides:
y = 5
The solution is x = -1 and y = 5.
We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
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explain the difference between a parameter and a statisitc, explain the difference between p and p hat, what is maent by sampling variabiloty
The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.
Parameter and statistic: Parameter is a value that describes the population, while statistic is a value that describes a sample.
Parameters are usually represented using Greek letters, while statistics are usually represented using Roman letters. In other words, a parameter is a population characteristic, whereas a statistic is a sample characteristic.
P and p hat: P represents the true proportion of a population with a particular attribute, while p hat represents the proportion of a sample with that attribute. P hat is an estimate of the true proportion p, which may differ from the actual proportion due to sampling error.
Sampling variability: Sampling variability is the variation in sample statistics that occurs from sample to sample. It is the result of the fact that different samples of the same size drawn from the same population will produce different estimates of the population parameter due to random sampling error. The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.
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An anthropologist is interested in the relationship
between fathers' and sons' heights. She collects a
simple random sample of 25 fathers and 25 sons, and
determines that the least-squares regression line is ý = -
2.8+ 1.1x, where ŷ is the predicted height of each son
and x is the height of his father (both measured in
inches).
One father is 72 inches tall, and his son is 75 inches tall.
What is the residual for the son's height?
O -2.8
O-1.4
O 1.1
O 1.4
Answer: B. -1.4
Step-by-step explanation:
To find the residual, we need to first calculate the predicted height of the son using the given regression equation:
ŷ = -2.8 + 1.1x
where x is the height of the father. For the given father who is 72 inches tall, we have:
ŷ = -2.8 + 1.1(72) = 75.6
So the predicted height of the son is 75.6 inches.
The residual is then calculated by subtracting the predicted height from the actual height of the son:
residual = actual height - predicted height
= 75 - 75.6
= -0.6
Therefore, the residual for the son's height is -0.6, which is closest to answer B after rounding to one decimal place.
How much bigger is 5x2y2 - 18xy2 - 10x2y
than -5x2 + 6x2y - 7xy ?
By using subtraction of polynomial, The polynomial 5x2y2 - 18xy2 - 10x2y is bigger by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 than -5x2 + 6x2y - 7xy.
To find the difference between 5x^2y^2 - 18xy^2 - 10x^2y and -5x^2 + 6x^2y - 7xy, we simply subtraction of polynomial the second expression from the first expression:
(5x^2y^2 - 18xy^2 - 10x^2y) - (-5x^2 + 6x^2y - 7xy)
= 5x^2y^2 - 18xy^2 - 10x^2y + 5x^2 - 6x^2y + 7xy (distributing the negative sign)
= 5x^2y^2 - 10x^2y + 5x^2 - 18xy^2 - 6x^2y + 7xy (rearranging terms)
= 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2 (combining like terms)
Therefore, the expression 5x^2y^2 - 18xy^2 - 10x^2y is bigger than -5x^2 + 6x^2y - 7xy by 5x^2y^2 - 16x^2y + 5x^2 - 18xy^2.
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Elijah is selling long sleeve t-shirts ( x ) and short sleeve t-shirts ( y ) for his family reunion in Charleston. The long sleeve t-shirts cost $27 each and the short sleeve t-shirts cost $20 each. Elijah collected $543 for all the t-shirts he sold. If Elijah sold 15 short sleeve t-shirts, how many long sleeve t-shirts did he sell? Write an equation to model the situation: x + y = How many long sleeve t-shirts did Elijah sell?
Answer: 9
Step-by-step explanation:
Let's first represent the given information in the form of an equation. We know that the long sleeve t-shirts (x) cost $27 each, and the short sleeve t-shirts (y) cost $20 each. Elijah collected $543 in total. So we can write the equation as:
27x + 20y = 543
We also know that Elijah sold 15 short sleeve t-shirts (y), so we can plug that value into the equation:
27x + 20(15) = 543
Now, we solve for x:
27x + 300 = 543
Subtract 300 from both sides of the equation:
27x = 243
Now, divide by 27:
x = 9
So Elijah sold 9 long sleeve t-shirts.
Number of long sleeve t shirts that Elijah sell is 9 long sleeve t shirts.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given that,
The long sleeve t-shirts cost $27 each and the short sleeve t-shirts cost $20 each.
He collected a total of $543.
So, we get an equation,
27x + 20y = 543
Also, given that, Elijah sold 15 short sleeve t-shirts.
Substitute y = 15.
27x + (20 × 15) = 543
27x + 300 = 543
27x = 543 - 300
27x = 243
x = 9
Hence Elijah sold 9 long sleeve t shirts.
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Which image shows a pair of similar polygons?
Answer: A
Step-by-step explanation:
A polygon is a plane figure with at least three straight sides and angles, and typically five or more. A matches with the description best.
(Sorry if you get this wrong..)
Polynomial function compared to an Exponential function
Given a polynomial function f(x) = 2x2 + 7x + 6 and an exponential function g(x) = 2x + 5, what key features do f(x) and g(x) have in common?
a. Both f(x) and g(x) increase over the interval of [–4 , [infinity])
b. Both f(x) and g(x) have the same x-intercepts of (–2, 0) and (–1.5, 0). c. Both f(x) and g(x) have the same y-intercept of (0, 6). d. Both f(x) and g(x) have the same range of (–[infinity], 0].
Step-by-step explanation & Answer:
It's easier to compare two functions if you can compare them by graphs.
The first function is a polynomial function - try your best to put these in standard form so that you can see where the roots/x-intercepts are. You can set the function equal to zero to find the roots, as well as set x=0 to find our y-intercept.
The second function is an exponential function. These always diverge ("shoot off") to positive infinity on the y-axis, and are asymptotic on the x axis, diverging to negative infinity. The only difference is made by a +5 here...that is a ENTIRE vertical shift up of 5 units <— Answer! Exponential functions also have a special y-intercept...think about what will happen if this intercept is shifted up 5 units.
! Know the forms of these two functions and how to graph them and it will make them much easier to compare !
if one of the 1127 people is randomly selected, find the probability that the person is a man or a heavy smoker
The required probability of randomly selected person to be a man or a heavy smoker is given by 0.5525.
Total number of people is equals to 1124
Total number of men is equals to 531
Total number of heavy smoker is equals to 90
Man and Heavy smoker are mutually exclusive events.
Let 'M' represents man
And 'H' represents heavy smoker
Probability of randomly selected person is a man or a heavy smoker
= P( M ∪ H )
= Probability of a man + Probability of a heavy smoker
= P( M ) + P (H)
= ( 531 / 1124 ) + ( 90 / 1124 )
= ( 621 / 1124 )
= 0.5525
Therefore, the probability of a person to be a man or a heavy smoker is equals to 0.5525.
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The above question is incomplete, the complete question is:
If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker.
table is attached.
scientific notation for 121000
A right triangle has one angle that measures 67°. What is the measure of the other acute angle?
Answer:
23 degrees
Step-by-step explanation:
Sum of all angles in a triangle add up to 180.
Right triangle consists of three angles, one a right angle which is a 90 degree angle and two other angles.
Therefore, 67+90 = 157. 180-157 = 23.
23 degrees
When the point (5, 5) is transformed using a translation, the result is point ( -1, 11). Complete the function below.
Answer: (x,y) = (-6, 6)
Step-by-step explanation: I'm not very good at explaining but if you you follow this equation, (x1-x2, y1-y2) with (x1,y1) (5,5) and (x2,y2) being the function, that's how you get (-1,11)
What are the solutions to the equation 2x2 + 12x =26
The solutions to the equation 2x² + 12x = 26 are x = -7 and x = 1.
How to solve equation?
To solve the equation 2x² + 12x = 26, we need to bring all the terms on one side of the equation and then factorize or use the quadratic formula to find the values of x that satisfy the equation.
First, we can simplify the equation by dividing both sides by 2 to get:
x² + 6x = 13
Now, we can bring all the terms to one side by subtracting 13 from both sides:
x² + 6x - 13 = 0
To factorize the quadratic expression, we need to find two numbers that multiply to give -13 and add to give 6. These numbers are 7 and -1, since 7 * -1 = -7 and 7 + (-1) = 6. So we can rewrite the equation as:
(x + 7)(x - 1) = 0
Now we can use the zero product property to find the values of x that satisfy the equation:
x + 7 = 0 or x - 1 = 0
Solving for x in each equation, we get:
x = -7 or x = 1
Therefore, the solutions to the equation 2x² + 12x = 26 are x = -7 and x = 1.
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8. Jake wants to buy the foam gymnastic block shown. If the
foam used to make the gymnastic block costs $24.99 per
cubic foot, what is the cost of this block, to the nearest
dollar?
After answering the provided question, we can conclude that Therefore, cuboid the cost of the gymnastic block is $225.
what is cuboid?A cuboid is a solid or three-dimensional shape in geometry. A cuboid is a convex polyhedron with 8 coordinates, 12 sides, but rather 6 rectangular faces. A cuboid is another name for it. A box is a cuboid because it has six square faces. Objects unearthed in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a capsule are perfectly straight and equal in size. But even though the structures of both the cube and cuboid are similar, they differ significantly in terms of side length, horizontal, and area.
the volume of the block is:
Volume = length x width x height
Volume = 2 ft x 3 ft x 1.5 ft
Volume = 9 cubic feet
Now, to find the cost of the block, we can multiply its volume by the cost of foam per cubic foot:
Cost of block = Volume x Cost per cubic foot
Cost of block = 9 cubic feet x $24.99 per cubic foot
Cost of block = $224.91
Therefore, the cost of the gymnastic block is $225.
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50 Points!!! Is there difference between the RHS Congruence Rule and Hypotenuse-Leg Theorem? If so explain why.
Yes, there difference between the RHS Congruence Rule and Hypotenuse-Leg Theorem.
The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side. In order to prove any two right triangles congruent, we apply the HL (Hypotenuse Leg) Theorem or the RHS (Right angle-Hypotenuse-Side) congruence rule.
Anyone know how to do this
The length of AD is approximately 9.2 units.
Describe Triangles?A triangle is a geometric figure that is formed by three line segments joining three non-collinear points in a plane. It is a three-sided polygon and the most basic two-dimensional shape. A triangle has three interior angles and three vertices. The sum of the interior angles of a triangle is always 180 degrees, and each angle is measured in degrees. Triangles can be classified based on the length of their sides and the measures of their angles. There are several types of triangles such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are used in various fields such as engineering, architecture, mathematics, and physics, and they are an essential part of many geometric calculations and constructions.
To solve this problem, we can use the angle bisector theorem which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides.
Let AD = x. Then we can set up the following proportion:
AC/CD = AB/BD
Substituting the given values, we get:
24/x = 15/(18 - x)
Simplifying this equation, we get:
360 - 15x = 24x
39x = 360
x = 9.23 (rounded to the nearest tenth)
Therefore, the length of AD is approximately 9.2 units.
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20 POINTS QUICK PLEASE What's the answer to the question using the information provided in pink? Also the destination is France with 67,750,000 people
4 Mastery Test Select the correct answer. A company manufactures school desks. The table shows the number of units that the company sold each month over a nine-month period beginning in January. Month, x Units, y Which equation best models the situation? 1 800 y = y = 7x + 450 34x² O A. O B. O C. y = -7x + 450 O D. y = -34x² + 334z + 1,075 2 500 - 3 400 334 + 1,075 4 300 5 200 Reset 6 7 300 450 Next 8 600 9 800
An equation that best models the situation include the following: A. y = 34x² - 334x + 1075.
How to determine an equation of the line of best fit?In order to determine an equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the number of months would be plotted on the x-axis of the scatter plot while the units would be plotted on the y-axis of the scatter plot.
Based on the scatter plot (see attachment) which models the relationship between the number of months and units, an equation for the line of best fit is given by:
y = 34x² - 334x + 1075
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This is the same information from the previous question.
The equation for the period of a pendulum is given by T space equals space 2 straight pi square root of straight L over 32 end root where T is the time (in seconds) and L is the length of the pendulum (in feet).
Find the approximate length of a pendulum if its period is 10 seconds.
The approximate length of the pendulum is 255.96 feet.
What is calculus?Calculus is a branch of mathematics that deals with the study of change and how things change over time.
We have the equation for the period of a pendulum as:
T = 2π√(L/32)
We need to find the length of the pendulum, L, if the period is 10 seconds. Rearranging the equation, we get:
L = 32(T/2π)²
Substituting T = 10, we get:
L = 32(10/2π)²
L ≈ 255.96 feet
Hence, the approximate length of the pendulum is 255.96 feet.
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a slice of a pie weighs 8 ounces. how many pounds do 6 slices of pie weigh? (2 points)2 pounds3 pounds4 pounds5 pounds
Answer:
3 Pounds
Step-by-step explanation:
If 1 slice of pie = 8 ounces that means that 6 slices would be 48 ounces because of 6 slices * 8 ounces. Now we have to take the 48 ounces and divide them by 16 because 16 ounces = 1 pound. And in doing so, 6 slices would = 3 Pounds.
At the start of the month, Carter had a total of $50 in his bank
account. During the month, he made deposits totaling $150. At the
end of the month, Carter still had a total of $50 in his bank account.
Based on this, which statement must be true?
The statement that must be true is: Carter withdrew or spent $150 during the month.
What is deposits ?
Deposit is money held in a bank account or with another financial institution that requires a transfer from one party to another.
If Carter had a total of $50 in his bank account at the start of the month and made deposits totaling $150 during the month, then he had a total of $200 in his account during the month.
Since he still had a total of $50 in his account at the end of the month, it means that he must have spent or withdrawn $150 during the month, which is equal to the total amount of deposits he made.
Therefore, the statement that must be true is: Carter withdrew or spent $150 during the month.
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HELP ME PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
Step-by-step explanation
wow, never seen this before
Paisley invested $16,000 in an account paying an interest rate of 8 3/8% compounded
monthly. Jayden invested $16,000 in an account paying an interest rate of 8 5/8%
compounded annually. To the nearest dollar, how much money would Paisley have
in her account when Jayden's money has tripled in value?
Paisley would have about $48147 in her account when Jayden's money has tripled using compounding.
What is compounding ?
In mathematics, compounding refers to the process of adding interest to an investment or loan, such that the interest is earned on both the principal amount and any previously accumulated interest.
First, let's find out how many years it will take for Jayden's money to triple in value. We can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where:
A = final amount
P = principal (starting amount)
r = interest rate (as a decimal)
n = number of times compounded per year
t = number of years
For Jayden, P = $16,000, r = 8.625% = 0.08625, n = 1 (compounded annually), and we want to find t when A = 3P = $48,000. Plugging in these values, we get:
[tex]\$48,000 = \$16,000(1 + 0.08625/1)^{(1t)[/tex]
[tex]3 = 1.08625^t[/tex]
[tex]ln(3) = t*ln(1.08625)[/tex]
[tex]t = ln(3) / ln(1.08625)[/tex]
t ≈ 13.2 years
So it will take about 13.2 years for Jayden's money to triple in value.
Next, let's find out how much Paisley will have in her account after the same amount of time, using the formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
For Paisley, P = $16,000, r = 8.375% = 0.08375, and n = 12 (compounded monthly). Plugging in t = 13.2 years, we get:
[tex]A = \$16000*(1 + 0.08375/12)^{(12*13.2)[/tex]
A ≈ $48147
Therefore, Paisley would have about $48147 in her account when Jayden's money has tripled in value, to the nearest dollar.
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Question 14(Multiple Choice Worth 2 points)
(Rewriting Rational Numbers LC)
Choose the numbers that are equivalent to 2-
15
14
15
14
15
37
12
37
15
2.46 246.6%
2.715, 271.5%
2.46 246.6%
2.715, 271.5%
What is the approximate volume of the sphere? use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary. responses 48 cm³ 48 c, m³ 150.72 cm³ 150.72 c, m³ 288.00 cm³ 288.00 c, m³ 904.32 cm³ 904.32 c, m³ sphere with dotted line extending from middle point of sphere to edge. line is labeled six centimeters.
The volume of the sphere is option (d) 904.32 cm³
Volume is a measure of the amount of three-dimensional space occupied by a substance, object, or region of space
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.
Substituting r = 6 cm and π ≈ 3.14 into the formula, we get:
V = (4/3) × 3.14 × 6³
Find the cube of the number
V = (4/3) × 3.14 × 216
Multiply the numbers
V ≈ 904.32
Rounding the answer to the nearest hundredth, we get approximately 904.32 cm³.
Therefore, the correct option is (d) 904.32 cm³.
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The given question is incomplete, the complete question is:
What is the approximate volume of the sphere when the radius is 6 cm?
Use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary.
a) 48 cm³
b) 150.72 cm³
c) 288.00 cm³
d) 904.32 cm³
Which scenario best illustrates a violation of substantive due process?
A. A city council passes a law that imposes a fine for vandalizing
public property.
B. A new law fines book publishers for printing content that is
considered unpatriotic.
C. A police officer decides not to give a man a ticket even though he
is speeding.
D. A drug dealer with several prior convictions is sent to prison
without a trial.
A violation of substantive due process (B)A new law fines book publishers for printing content that is considered unpatriotic. A drug dealer with several prior convictions is sent to prison without a trail.
The procedural rights guaranteed by the United States Constitution ensure that all citizens are treated equally before the law. For example, all citizens have the right to a lawyer, to a public and speedy trial, to have their case judged by a jury of their peers, etc.
In Scenario B, the drug dealer's rights are violated by law enforcement. Even if he has a criminal record, law enforcement has no right to immediately throw him in jail.
Due process is the application of all legal rules and principles relating to a case by the state to uphold all legal rights of individuals. Due process balances the power of the laws of the land and protects individuals against the laws. When the government harms a person without following the exact procedure of the law, it is a violation of due process and violates the rule of law.
It is the constitutional process in which the federal government before denying a citizen the right to life, liberty, or freedom, must give proper notice to the person, the opportunity of being heard, and the decision is taken without any discrimination. The act which violates the Procedural due process is giving a driver a traffic ticket without telling him, his right, i.e, can appeal in court against it.
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help me solve this a it is do tomorrow. for 12 points
2 3/7+4 6/7=
2 1/6-1 5/6=
After solving the given fraction 2 3/7+4 6/7, the resultant answer is 51/7.
What are fractions?Fractions represent any number of parts of a whole, or more generally equal parts.
In everyday English, fractions represent how many parts of a particular size there are. 8, 3/4.
Fractions represent a whole object or part of a collection.
A fraction consists of two parts. The number at the top of the line is called the counter. Indicates how many equal parts of the whole or collection are taken.
The number below the line is called the denominator.
So, solve the fractions as follows:
= 2 3/7+4 6/7
= 14+3/7 + 28+6/7
= 17/7 + 34/7
= 17+34/7
= 51/7
Therefore, after solving the given fraction 2 3/7+4 6/7, the resultant answer is 51/7.
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Complete question:
Solve the fractions: 2 3/7+4 6/7
What is the perimeter, in centimeters, of a rectangle with vertices located at (−20, 14), (8, 14), (−20, −4), and (8, −4)?
260 cm
92 cm
72 cm
46 cm
Answer:
92 cm
Step-by-step explanation:
From (-20, 14) to (8, 14) the distance is 20 + 8 = 28
From (-20, 14) to (-20, -4) the distance is 14 + 4 = 18
perimeter = 2(length + width)
perimeter = 2(28 + 18)
perimeter = 2(46)
perimeter = 92
Answer: 92 cm
What is the surface area of a rectangular prism with a length of 6.8 a width of 1.6 and a height of 3.8 work shown please
Answer:
85.6 square units.
Step-by-step explanation:
The surface area of a rectangular prism is the sum of the areas of all six faces. To find the surface area of the given rectangular prism, we can use the formula:
Surface Area = 2lw + 2lh + 2wh
where "l" is the length, "w" is the width, and "h" is the height.
Substituting the given values, we get:
Surface Area = 2(6.8)(1.6) + 2(6.8)(3.8) + 2(1.6)(3.8)
= 21.76 + 51.68 + 12.16
= 85.6
the surface area of the rectangular prism is 85.6 square units.
Find the total value of the investment after the given time period.
$5000 at 2.5% for 8 years compounded monthly.
Question 8 options:
$6,105.74
$5,083.94
$6,103.21
$5,101.00
To find the total value of the investment after 8 years with monthly compounding, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the given values, we get:
A = 5000(1 + 0.025/12)^(12*8)
A ≈ $6,105.74
Therefore, the total value of the investment after 8 years is approximately $6,105.74.
So, the correct option is (a) $6,105.74.
Help i will give you Brainly
Answer:
Mode = 25
Median = 29
Mean = 30.3
Range = 36
Step-by-step explanation:
To find the mode, order the numbers lowest to highest and see which number appears the most often.
To find the median, calculate the mean by adding together the middle values and dividing them by two.
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
Use the parallelogram to the right to find the measure of
PLS HELP THIS IS URGENT!!!!!!!!
this is geometry
Answer:
The value of A is 62
Step-by-step explanation:
since it is parallel to C