[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\mathbb{R}50000\\ r=rate\to 0.5\%\to \frac{0.5}{100}\dotfill &0.005\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A = 50000\left(1+\frac{0.005}{1}\right)^{1\cdot 20}\implies A=50000(1.005)^{20} \implies \boxed{A \approx 55244.78} \\\\\\ 55244.78~~ - ~~50000 ~~ \approx ~~ \stackrel{earned~interest}{\boxed{5244.78}}[/tex]
DJ is riding in the passenger seat of a car that is going 40 miles per hour
when it passes Jabari, who is standing on the street. From Jabari's
perspective, how quickly is DJ moving?
A
DJ does not appear to be moving at all.
B. DJ appears to be moving more slowly than the car.
C. DJ appears to be moving more quickly than the car.
D. DJ appears to be moving at the same speed as the car.
Answer: DJ appears to be moving at the same speed as the car
Step-by-step explanation:
DJ is inside of the car, so he moves with it. Jabari is outside of the car and is standing still, so both DJ and the car he is in seems to be moving at 40 miles per hour at the same time
The vertices of YEAR are Y(1,-4) E(3,0), A (-1,2) and R( -3,-2) . prove that YEAR is a Square
To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).
Side Lengths: To find the lengths of the sides, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
For example, to find the length of the side that connects Y and E, we can use the following calculation:
d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20
We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.
A map scale designates 1 inch = 25 km. The distance between the two towns on the map is 3 inches. If a liter of gasoline can last you for 50 kilometers, how many liters of gasoline would you need to drive from the first town to the second?
The amounts of liters of gasoline that you need to drive from the first town to the second is given as follows:
1.5 liters.
How to obtain the amount of gasoline needed?The amount of gasoline needed is obtained using the proportions in the context of this problem.
The scale is given as follows:
1 inch = 25 km.
Meaning that each inch on the drawing represents an actual distance of 25 km, then the actual distance of the towns separated by 3 inches on the map is given as follows:
3 x 25 = 75 km.
A liter of gasoline lasts for 50 kilometers, hence the amount of liters of gasoline needed for 75 kilometers are given as follows:
75/50 = 1.5 liters.
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
The surface area of the rectangular prism is 100m²
How to determine the surface areaThe formula for calculating the surface area of a rectangular prism is expressed as;
Surface area = 2(wl + hw + lh)
Given that;
w is the width of the rectangular primsh is the height of the rectangular prisml is the length of the rectangular prismFrom the diagram shown, let's substitute the values, we have;
Surface area = 2(2× 7 + 4× 2 + 7 × 4)
multiply the values, we get;
Surface area = 2(14 + 8 + 28)
Add the values
Surface area = 2(50)
Expand the bracket
Surface area = 100m²
Hence, the value is 100m²
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What is
√12x8/√3x²
in simplest form, where x>0?
The simplest form of √12x⁸/√3x² is 2x³.
What is simplification?
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Here, we have
Given: √12x⁸/√3x²
We have to simplify this function.
We combine both terms in one and we get
= √12x⁸/3x²
= √4x⁶
= 2x³
Hence, the simplest form of √12x⁸/√3x² is 2x³.
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what is the value of Z?
The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414. This value is widely used in mathematics.
What is the value of 2√ 2 ?Well, the basic answer is that the value of root 2 (i.e., 2) is 1.412. We must first understand the concepts of power and roots in order to comprehend what root 2 (2) is and how to calculate its value. √2 = 1.414
You may determine the values of non-perfect square values like root 3, root 5, etc. using the long division method.
The square root or root of a number "n" is a number that, when multiplied by itself, has the value "n". For instance, the square root of 4 is equal to 2. thus 2 + 2 Equals 4. The opposite of squaring a number is finding the square root of that integer.
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Annie is helping you graph the line y - 3 = 2(x + 1).
She tells you to follow the steps below.
Step 1: Plot the point (1, -3).
Step 2: Plot more points by moving up 2 and right 1.
Step 3: Draw a line through the points and put arrows on the ends..
Annie made a mistake.
What was her mistake? How should she fix her mistake?
Answer: Annie made a mistake in step 1 by plotting the point (1, -3) instead of (1, 0) which is the x-intercept of the given equation.
Step-by-step explanation:
She should have used the x-intercept of the equation instead of just any point.
To fix her mistake, Annie should find the x-intercept of the equation by setting y to 0, and solve for x. Then she can plot the point (1,0) and proceed with step 2 and 3.
Does someone mind helping me with this problem? Thank you!
The total number of $12 tickets are 120 while the $15 tickets are 180.
What is algebraic expression?In addition to using operational signs, algebraic expressions also include numbers and variables. Examples include multiplication, multiplication with the natural exponent, division, and addition, subtraction, and exponentiation. The term "fractional expression" refers to division in an algebraic expression with variables.
The term "rational numbers" refers to numbers that can be expressed as fractions. Integers, repeating decimals, and terminating decimals are a few examples.
Given that x stands for $12 tickets and y stands for $15 given as the equation
12x + 15y = 4140
x + y = 300
y = 300 - x
Substitute the value of y in the first equation
12x + 15(300 - x) = 4140
12 x + 4500 - 15x = 4140
12x - 15x = 4140 - 4500
-3x = −360
x = 360/3
x = 120
y = 300 - (120)
y = 180
Thus, The total number of $12 tickets are 120 while the $15 tickets are 180.
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the maller of 2 conecutive number i x3
a.find the um of the two number
b.find their difference
c.ubtract their um for x8
The sum of the two consecutive numbers is 31.
Let the two consecutive number are n and n+1.
Given the difference between square of two consecutive Numbers is 31.
(n + 1)² - n² = 31n² + 2n + 1 – n² = 312n + 1 = 312n = 30n = 15Then, two consecutive number = n, n+1 = 15, 16
Therefore
( A ): the sum of two consecutive number = 15 + 16 = 31
( B ): Their difference = 16 – 15 = 1
( C ): Subtract their sum by 8 = 31 – 8 = 23
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convert 6 2/5 to a fraction greater than 1
Answer:
Step-by-step explanation:
6 2/5
Number 5 is denominator, keep it for denominator.
Numerator will be 6x5+2 =32
so, a fraction of 6 2/5 greater than 1 is 32/5
3. Which represents the least percent of change?
A. A $125 watch selling for $90.
B. The speed limit changing from
40 mph to 55 mph.
C. The stock market dropping from
250 to 175 points.
D. Marissa's math grade increasing
from 75 to 99.
Answer: B. The speed limit changing from 40 mph to 55 mph represents the least percent of change.
In A, a watch selling for $90 from $125 represents a 28% decrease,
In C, the stock market dropping from 250 to 175 points represents a 30% decrease,
In D, Marissa's math grade increasing from 75 to 99 represents a 32% increase.
While in B, the speed limit changing from 40 mph to 55 mph represents a 37.5% increase.
So, B represents the least percent of change.
Step-by-step explanation:
Ben and tom each take driving test. The probability that ben and tom will pass is 0. 87 and 0. 7 respectively
The probability that ben and tom will pass is 0. 87 and 0. 7 respectively will be 0.38
The answers to the questions are as follows:
Please refer to the attached file for point a.
Since both of them pass their driving tests at the same time, we double the odds of each one passing, which results in a probability of "56%".
Tom passes but Ben fails, or Tom passes but Ben succeeds. Therefore, the likelihood and the response is "38%."
(a)The tree diagram is attached.
P(Ben Fails)=1-0.8=0.2
P(Tom Fails)=1-0.7=0.3
(b)Probability that both will pass their driving test.
P(both will pass)=0.8 X 0.7 =0.56
(c)Probability that only one of them will pass their driving test.
P(Tom Bass, Ben Fails OR Ben Pass, Tom Fails)
=(0.7 X 0.2)+(0.8 X 0.3)
=0.14+0.24
=0.38
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Change 9 out of 20 to a percentage.
Answer:
45%
Step-by-step explanation:
Answer:
45%
Step-by-step explanation:
[tex]\frac{9*5}{20*5}[/tex] = [tex]\frac{45}{100}[/tex]
Drag each tile to the correct box. Consider the given circles. Sector B 9 units 820 Sector c Sector A 6 units 1690 4 units Order the sectors from least to greatest according to their areas, in square units. Sector C Sector B Sector A A
The order from least to greatest is: A, B, C
The order of the sectors from least to greatest according to their areas is:
Sector A, Sector B, Sector C
To find the area of each sector, we need to multiply the central angle measure (in degrees) by the radius squared and divide by 360.
Sector A: 4 units * (1690 / 360) = 46 square units
Sector B: 6 units * (820 / 360) = 69 square units
Sector C: 9 units * (820 / 360) = 103.5 square units
Hence, the order from least to greatest is: A, B, C
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PLEASE HELP!! A ladder is leaning against a wall. What is the length of the ladder if it is resting against the wall at a height of 48 feet and it forms an angle of 53 degrees with the ground? Round your answer to the nearest tenths place
The length of the ladder, if it is resting against the wall at the height of 48 feet and it forms an angle of 53 degrees with the ground being 63.7 ft.
First, we need to draw a figure according to the conditions given in the question.
Now, let AC be the length of the ladder, AB is the length of the wall, and BC is the length of the ground, as shown in the figure.
As we know,
tan θ = perpendicular/hypotenuse
tan 53 = AC/AB
AC = tan 53 × AB
AC = 1.327 × 48
AC = 63.7 ft
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Please answer!!! The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drink
The equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
The inspector at a bottling plant checks 25 bottles, and two bottles do not pass inspection.
To find the amount of sports drinks in milliliters that pass inspection, we can subtract the amount in the two bottles that do not pass inspection from the total amount in all 25 bottles.
Let x be the amount of sports drinks in milliliters in each bottle.
The expression for the milliliters of sports drink that pass inspection is = 25x - 2x
Now, simplifying the expression, we get,
25x - 2x = (25-2)x = 23x
Hence, the equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
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The complete question is -
The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drinks. Write an expression for the milliliters of sports drink that pass inspection. Then simplify it to create an equivalent expression.
Are 3/8 and 3/4 equivalent fractions with a number line
A family ha two car. The firt car ha a fuel efficiency of 35 mile per gallon of ga and the econd ha a fuel efficiency of 15 mile per gallon of ga. During one particular week, the two car went a combined total of 1150 mile, for a total ga conumption of 50 gallon. How many gallon were conumed by each of the two car that week?
The first car consumed 35 number of gallons and the second car consumed 15 gallons.
1. Calculate the total efficiency of both cars: 35 mpg + 15 mpg = 50 mpg
2. Calculate total gallons consumed: 1150 miles/50 mpg = 23 gallons
3. Divide total gallons by each car: 23/2 = 11.5 gallons (round down to 11 for the first car and round up to 12 for the second car)
4. The first car consumed 11 gallons and the second car consumed 12 gallons.
The first car consumed 35 gallons and the second car consumed 15 number of gallons.
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Pls solve 5^2x-1–6(5^x) + 25=0
Write and compound inequality-4 is greater than x and less than 2
The compound inequality is x<-4 and x<2.
What is a compound inequality?
A compound inequality in mathematics is a clause that joins two claims with the conjunction "and" or "or." Both of the statements in a compound sentence are true simultaneously if the conjunction "and" is used to connect the statements. If "or" is used to connect the statements, the compound phrase is true if at least one of the statements is true.
We are given that -4 is greater than x
This means that -4>x
Also, it is given that x is less than 2
Therefore, x<2
Hence, the compound inequality is x<-4 and x<2.
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Which is a correct solution for the following system of Inequalities
The solution for given linear inequalities is (-0.5,4.25) from the given graph.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
As we know the solution for the lines which intersect at a certain point is that point or the coordinates of that point i.e. (-0.5,4.25).
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A toy store had 4 boxes that weighed a total of 34 kilograms. If each box had the
same amount of weight, how much did each box weigh? Between what two whole
numbers does your answer lie?
The weight lies between the whole numbers 8 and 9.
The length, breadth, and height of a package are multiplied using the longest point on each side to determine the dimensional (DIM) weight.
If each of the 4 boxes has the same weight, the weight of each box can be found by dividing the total weight by the number of boxes. Given that the total weight is 34 kilograms, the weight of each box is:
w = 34 kg / 4 boxes = 8.5 kg
So, each box weighs 8.5 kilograms. The weight lies between the whole numbers 8 and 9.
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What number is 24 less than 3 times itself?
Answer:
3x - 24
Step-by-step explanation:
24 less is the same as: - 24
3 times itself is: 3x
Tamisha works as an intern in an architect’s office. A designer drew a scale drawing of a kitchen without using grid paper. In the drawing, 1 inch represents 2 1/2 feet. Tamisha’s supervisor wants her to determine the skill factors for the length and the skill factors for the areas of.
a. Find the scales factor for the lengths
b. Find the scales factors for the areas
Answer:
length: 1:30, area: 1:900
Step-by-step explanation:
1ft = 12 inches, so 2.5' = 30". scale for length is 1:30, for area it's square - 1:900
. What crimes do these excerpts from the Code of Hammurabi identify?
Which of those are considered crimes today? Which are not?
3) What punishments do these excerpts from the Code of Hammurabi identify?
4) Which of those punishments are used today? Which are not?
5) Based on these short excerpts from the code, how do you think Hammurabi defined justice?
6) In what ways do our codes of law today show similarities to and differences from the concept of justice as shown in these short excerpts from Hammurabi’s Code?
7) In what ways has today's view of justice changed from Hammurabi's? What events and ideas do you think caused these changes?
1. These excerpts from the Code of Hammurabi identify crimes such as theft, assault, and damage to property.
2. Some of these crimes, such as theft and assault, are still considered crimes today. However, some of the punishments specified in the code, such as the punishment for a son striking his father, would not be considered appropriate today.
3. These excerpts from the Code of Hammurabi identify punishments such as fines, imprisonment, and physical punishment such as whipping or amputation.
4. Physical punishments such as whipping or amputation are no longer used in most modern legal systems.
5. Fines and imprisonment are still used as punishments today.
6. Based on these short excerpts from the code, it seems that Hammurabi defined justice as a system of strict punishment for crimes, with different punishments for different classes of people and different severity of crimes.
Our codes of law today show similarities to the Code of Hammurabi in that they both have a system of punishment for crimes. However, there are also many differences, such as the fact that our legal system is considered more fair and equal, and places a greater emphasis on rehabilitation and protecting the rights of the accused.
7. Today's view of justice has changed significantly from Hammurabi's in that it places a greater emphasis on protecting the rights of the accused, rehabilitation, and equality before the law. This change can be attributed to a number of factors, including the development of democratic societies, the influence of human rights movements, and the advancement of legal scholarship and philosophy.
What is Hammurabi code?The 282 rules that make up the Hammurabi code of laws established norms for business dealings and established fines and penalties to satisfy the demands of justice.
A large, finger-shaped black stone stele with Hammurabi's Code carved on it was looted by invaders and only recently found in 1901. One of the most well-known examples of the ancient maxim known as "lex talionis," or the law of retribution, is the Hammurabi Code.
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Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69
∘
∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
A right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.
What are right triangles?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
So, the parameters listed are:
69-degree angle.
Ladder length (l) equals 26 feet.
The following cosine ratio is used to compute the horizontal distance (h).
cos(θ) = h/l
Replace known values:
cos(69) = h/26
Make the topic "h":
h = 26 * cos(69)
Consider the product:
h = 9.3
Therefore, a right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.
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if 12% of a number is 75, find 4% of that number
Answer:
25.60
Step-by-step explanation:
first divide 12%of a number with 75 Ans will be 6.25 then multiply with 4 Ans will be 25.60
Answer: 25
Step-by-step explanation:
12 divided by 4 = 3
75 divided by 3 = 25
25 = 4%
the activity of a radioactive isotope is found to decrease by 40% in one week. what are the values of its: a) decay constant, b) half-life, c) mean lifetime?
Answer: A) The decay constant (λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability per unit time that an atom of the isotope will decay. The decay constant can be calculated using the formula:
λ = -ln(1 - x) / t
Where x is the fraction of the original activity that has decayed (in this case, 0.40), and t is the time over which the decay occurred (in this case, one week).
B) The half-life (T1/2) is the amount of time it takes for half of the original activity of a radioactive isotope to decay. It can be calculated using the formula:
T1/2 = ln(2) / λ
C) The mean lifetime (τ) is the average amount of time an atom of a radioactive isotope will survive before it decays. It can be calculated using the formula:
τ = 1 / λ
It's important to note that the above formulas are based on the exponential decay model, which assumes that the decay process is random and that the decay constant is constant over time. If the isotope does not decay in this way, these formulas may not give accurate results.
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!!!
The volume of an ice cream cone is the measure of how much ice
cream fits inside the cone. An ice cream cone company wants to
make an ice cream cone with a greater height that still holds the
same amount of ice cream.
Write an equation to calculate the volume of a cone.
Then rewrite the equation to solve for the height.
Explain how your equation determines a linear measurement when the original equation determined a cubic measurement
The volume of a cone is V = πr²h/3
The equation rewritten to solve for the height is V = πr²h/3
How to determine the equationIt is important to note that the formula for volume of a cone is expressed as;
V = πr²h/3
The parameters are;
V is the volume of the coneπ takes the constant value, 22/7 or 3. 142h is the height of the coneSince the ice cream fits inside the cone and the height still holds the ice cream, let's make the height subject of formula.
Let's take the following steps;
V = πr²h/3
cross multiply the equation, we get;
V × 3 = πr²h × 1
Multiply the values
3V = πr²h
To make the variable 'h' stand alone, let's divide both sides of the equation by its coefficient
3V/πr² = πr²h/πr²
Divide the values
c
Hence, the equation determines a linear measurement since the value 3 multiply the volume and not divides it.
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Find the length of x. Please help I will mark brainlist
Answer:
its 4, but give the other guy brainliest he answered first :D
Step-by-step explanation: