Answer:
Step-by-step explanation:
Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.
What is the increase in Fahrenheit temperature if the Celsius temperature increases by 7°?!
The increase in Fahrenheit temperature is of 12.6 degrees.
What is the increases in Fahrenheit temperature?The formula to have a change of units is:
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C x 1.8) + 32
(So you are correct, the rate is 9/5 = 1.8)
The increase of 7°C wold be given by the difference:
increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32
Solving that equation we can see that
increase = 12.6°F
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Answer:
he increase in Fahrenheit temperature is of 12.6 degrees.
What is the increases in Fahrenheit temperature?
The formula to have a change of units is:
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C x 1.8) + 32
(So you are correct, the rate is 9/5 = 1.8)
The increase of 7°C wold be given by the difference:
increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32
Solving that equation we can see that
increase = 12.6°F
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Step-by-step explanation:
A poll showed that 53.2% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Round to 3 decimal places.
The probability that a statistics teachers do not know the true meaning of life is 46.8%
What is the probability of someone who does not believeFrom the question, we have the following parameters that can be used in our computation:
53.2% of Americans say they believe that statistics teachers know the true meaning of life.
This means that
P(Believe) = 53.2%
For the required probability, we have
P(Not believe) = 1 - P(Believe)
So, we have
P(Not believe) = 1 - 53.2%
Evaluate
P(Not believe) = 46.8%
Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%
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4. Malaki has a 'no interest-free period' credit card that charges 16.5% p.a. interest. On 9 January he purchases a phone costing K395.00. His January statement is dated 28 January and the phone is the only item on it.
a. How much interest is charged on the January credit card statement?
b. Malaki pays K100.00 off the amount owed on 28 January and makes no more purchases or payments before the next credit card statement arrives on 28 February. How much will this statement show that Malaki owes?
Answer:
K5.60.
Step-by-step explanation:
Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
In 2016 , a clinical study in a small town of New Hampshire found that about 13 % of its population had the flu . The study also showed that 19 % of the people who had the flu tested negitive while 8% of of the people who did not have the flu tested positive . based on the given information construct a realative frequency table.
The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.
To get the relative frequencies, we divide each cell value by the total frequency of the table.
This is how we construct relative frequency table.
To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.
Let's define the following events:
A: a person has the flu
B: a person tests positive for the flu
Then, using the information given in the problem, we can construct the following relative frequency table:
A (has the flu) not A (does not have the flu) Total
B 0.13*0.81 = 0.1053 0.08*0.87 = 0.0696 0.1749
not B 0.19*0.81 = 0.1540 0.63*0.87 = 0.5471 0.7011
To 0.2843 0.6171 0.901
In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.
The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.
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Which of the following questions about a particular animal could NOT be answered using only the data collected for the tracking collars?
The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.
What are tracking collars?A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.
The functions of the tracking collars include the following:
It allows them to note how many miles the animal can travel in a given time.It allows them to note the pattern of movement of the animals.It allows them to note the location preferred by the animal to travel.Learn more about tracking here:
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Complete question:
Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.
The time
The date
The location of the animal
Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?
A. Approximately how many miles did the animal travel in one week?
B. Does the animal travel in groups with other tracked animals?
C. Do the movement patterns of the animal vary according to the weather?
D. In what geographic locations does the animal typically travel?
C. Do the movement patterns of the animal vary according to the weather?
An English class consists of 23 students, and three are to be chosen to give speeches in a school competition. In how many different ways can the teacher choose the team, given the following conditions? The order of the speakers is not important
Answer: The number of different ways the teacher can choose the team of three students from a class of 23, where the order of the speakers is not important, is 1771.
Step-by-step explanation:
To solve this problem, we can use the combination formula:
nCr = n! / r!(n - r)!
where n is the total number of items, r is the number of items to be selected, and ! represents factorial, which means the product of all positive integers up to the given number.
In this case, we need to choose 3 students out of 23, without regard to the order in which they will speak. Therefore, we need to use the combination formula with n = 23 and r = 3:
23C3 = 23! / (3!(23 - 3)!)
= 23! / (3!20!)
= (23 × 22 × 21) / (3 × 2 × 1)
= 1771
Therefore, there are 1771 different ways the teacher can choose the team of three students for the competition, where the order of the speakers is not important.
Given f(x)
, find g(x)
and h(x)
such that f(x)=g(h(x))
and neither g(x)
nor h(x)
is solely x.
f(x)=−square root of x+4 minus 3
The functions g(x) = -√x - 3 and h(x) = x + 4 meet the requirements, and f(x) = g(h(x)) is true for f(x) = -√(x+4) - 3.
We are given f(x) and we need to find functions g(x) and h(x) such that f(x) = g(h(x)). The given function is f(x) = -√(x+4) - 3.
To find g(x) and h(x), we can split the given function into two simpler functions. Let's first look at the inner function, which deals with the input of the square root. We can define h(x) as the function inside the square root, which is:
h(x) = x + 4
Now we need to find g(x) such that when h(x) is plugged into it, we get the original function f(x). Since we have the square root and a subtraction, we can define g(x) as:
g(x) = -√x - 3
Now let's verify if f(x) = g(h(x)):
g(h(x)) = g(x + 4) = -√(x + 4) - 3
As you can see, g(h(x)) = f(x), which confirms that the functions g(x) and h(x) we found satisfy the condition.
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Drop the ball from a height equal to one of your group member's height (high is 5.3)
Determine the amount of time the ball takes to touch the ground (with a timer)
Time to touch the ground: 1.08 seconds
Initial velocity of the ball: ) ft/sec
Plug the initial velocity and the time to touch the ground into:
-16t^2 + v X t+h=0
Solve your equation for h. Based on the height of the person you dropped the ball from, how accurate is your answer for h?
The time taken for the ball to touch the ground is 0.61 s.
What is the time of motion of the ball?The time taken for the ball to touch the ground is calculated by applying the following method.
-16t² + vt + h = 0
where;
v is the initial velocity of the ballh is the height of fall of the ballt is the time of motionwhen the height of the ball = 5.3 ft, with initial velocity = 1.08 ft/s, the time of motion of the ball is calculated as follows;
-16t² + vt + h = 0
-16t² + 1.08t + 5.3 = 0
16t² - 1.08t - 5.3 = 0
solve the quadratic equation, using formula method;
a = 16, b = -1.08, c = -5.3
t = 0.61 second.
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How to solve pre algebra?
Answer:
Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:
1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.
2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.
3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.
4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.
It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.
solve 5 to the power of x+2 is less than or equal to 3 to the power of x
Step-by-step explanation:
5^(x+2) <= 3^x
5^x * 5^2 <= 3^x
25 <= 3^x / 5^x
25<= (3/5)^x LOG both sides
log 25 <= x log (3/5)
log 25 / log (3/5) <= x
- 6.3 <= x
((46 – 15) × 32) + 5 =
Answer:
=997
Step-by-step explanation:
46-15=31
31×32=992
992+5=997
Answer: 997
Step-by-step explanation:
Alina wants to make keepsake boxes for her two best friends. She doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material.
For Jen, Alina wants to make a box with a square base whose sides and base are made of wood and whose top is made of metal. The wood she wants to use costs 5 cents per square inch, while the material for the metal top costs 12 cents per square inch. What is the largest possible box (in terms of volume measured in cubic inches) that Alina can make for Jen if she only has $30.00 to spend on materials? (Round your answer to three decimal places.)
Answer:
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Step-by-step explanation:
Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.
The surface area of the box (excluding the top) is given by:
2(x^2) + 4(x^2) = 6(x^2)
The surface area of the metal top is:
x^2
The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:
6(x^2) + x^2 = 7(x^2)
The cost of the wood for the box is:
5 cents per square inch * 6(x^2) = 30x^2 cents
The cost of the metal for the top is:
12 cents per square inch * x^2 = 12x^2 cents
The total cost of the box is:
30x^2 + 12x^2 = 42x^2 cents
We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:
42x^2 = 3000
Solving for x, we get:
x^2 = 71.429
x ≈ 8.445
Therefore, the maximum volume of the box is:
V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Simplify each of the following exponential expressions. a. 7⁴= ? b. (–10)⁴= ? c. 5¹ = ? d. 0⁴= ? e. –6²= ? f. –3⁰= ?
The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1
Simplifying each of the exponential expressionsFrom the question, we have the following parameters that can be used in our computation:
The exponential expressions a to f
The general rule is that
a^b = a * a * a..... in b places
Using the above as a guide, we have the following:
a. 7⁴ = 7 * 7 * 7 * 7 = 2401
b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000
c. 5¹ = 5
d. 0⁴ = 0 * 0 * 0 * 0
e. –6² = -6 * -6 = 36
f. –3⁰ = 1
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Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.
with the steps and explanation
Answer:
Step-by-step explanation:
The required probability is simply the (shaded area)/(area of the whole box)
The area of the whole box would be:
6r*2r = 12 r^2
The shaded area is tough to calculate, but you can get the
white area instead.
The left hole (white area) consists of a semi-circle and a rectangle.
The center hole is a circle.
The right hole (white area) consists of a semi-circle and a rectangle.
The 2 semi-circles in the left and right hole combine to be a circle.
The 2 rectangles in the left and right hole combine to be a square.
The total area of holes are:
(area of circle)*2 + (area of square) ### 2 circles 1 square in total
=r^2*pi*2 + (2r)^2
=r^2*pi*2 +4*r^2
then we can get the shaded area by:
(area of the whole box) - (The total area of holes)
= 12 r^2 - (r^2*pi*2 +4*r^2)
=8*r^2 - r^2*pi*2
Finally:
(shaded area)/(area of the whole box)
=(8*r^2 - r^2*pi*2)/(12 r^2)
=(8-pi*2)/(12)
=0.143067891
=14.3% (corr. to 3 sig. fig.)
The ratio of the reclusive to gregarious was 3 to 14. And 15,300 lived in the valley, how many were gregarious?
The ratio of gregarious that lived in the valley is 126,00
What is Ratio?Ratio is the comparison of two quantities of the same kind or for comparing two or more quantities that are measured in the same units. It is also is a relationship between two things when it is expressed in numbers or amounts.
How to determine this
The total who lived in valley = 15,300
The ratio of Reclusive = 3
The ratio of Gregarious = 14
And the ratio of reclusive gregarious = 3 : 14
The total ratio = 3 + 14 = 17
To calculate the total amount of gregarious
= 14/17 * 15,300
= 12,600
Therefore, the total amount of gregarious is 12,600
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simplify the expression 4√ 2 + 2√ 32? 12/2 6/32 12/32 36/2
The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
We know that,
An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, given expression is,
4√ 2 + 2√ 32
=4√ 2 + 2√ 16 × 2
we know that,
√16 = 4
so, we get,
=4√ 2 + 2√2 × 4
=4√ 2 + 8√2
=12√2
Hence, The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
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Identify the area of a regular hexagon with side length 14in. rounded to the nearest tenth.
The area of a regular hexagon with side length 14 inches is 509.22 square inches.
Given that, a regular hexagon with side length 14 inches.
We know that, area of a regular hexagon can be calculated using A=3√3/2 a².
Here, area of a regular hexagon = 3√3/2 ×14²
= 3√3 ×98
= 509.22 square inches
Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.
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If a fair coin is tossed twice the possible outcomes are HH, HT, TH or TT, where HH means both tosses are heads and HT means that the first toss is a head and the second toss is a tail, etc. Since the coin is fair, a 50-50 chance of getting a head or a tail, we assign a probability of 1/4 to each of the four outcomes. Assuming that a fair coin was tossed twice, find the probability that exactly one of the tosses is a head and the other toss is a tail.
Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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A mountain climber is at an elevation of 10,000 feet. If she descends 2,000 feet a day, which equation would be used to show how many days it will take to reach sea level (0 feet)?
-10,000 ÷ (-2,000)
-10,000 ÷ 2,000
10,000 ÷ 2,000
10,000 ÷ (-2,000)
Answer: The correct equation to use is, C. 10,000 ÷ 2,000
Which simplifies to: 5
Therefore, it will take 5 days for the mountain climber to descend from an elevation of 10,000 feet to sea level, assuming they descends at a constant rate of 2,000 feet per day.
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In each figure, all b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain
your answer.
미미미
a. Yes; it is one reflection after another with respect to the two parallel lines.
b. No; it is a reflection followed by a translation.
c. No; it is a reflection followed by a rotation.
d.
No; it is one reflection after another with respect to the two parallel lines.
Answer:
a
Step-by-step explanation:
5/3X + 1/3X= 2 2/3+ 8/3X
The solution of the given equation 5X/3 + X/3 = 2 (2/3) + 8X/3 is, X = - 4.
The equation is a mathematical statement involving mathematical variable, numerical values, mathematical operation with a equal sign.
The given equation is,
(5/3)*X + (1/3)*X = 2 (2/3) + (8/3)*X
Solving the equation we get,
5X/3 + X/3 = (2*3 + 2)/3 + 8X/3
5X/3 + X/3 - 8X/3 = (6 + 2)/3
(5X + X - 8X)/3 = 8/3
- 2X/3 = 8/3
- 2X = 8
X = 8/(-2)
X = - 4
Hence the solution is, X = - 4.
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A cyclist managed to ride 5 miles against the wind in the same time that it took him to ride 10 miles with the wind. If the wind speed is 4 mph, which equation can be used to calculate the cyclist’s average rate of speed in miles per hour?
Answer:
Step-by-step explanation:
Average Rate of Speed = Distance / Time
Average Rate of Speed = (5 + 10) / (Time with the Wind + Time Against the Wind)
Average Rate of Speed = 15 / (Time with the Wind + Time Against the Wind)
Average Rate of Speed = 15 / (10/4 + 10/6)
Average Rate of Speed = 15 / (2.5 + 1.67)
Average Rate of Speed = 15 / 4.17
Average Rate of Speed = 3.59 mph
The vector (6,-5) is reflected across the line y=x, and the resulting matrix is dilated by a scale of -1.5
(7.5, -9) is the final value after reflection and dilation.
To reflect a vector across the line y=x, we switch the x and y coordinates. Therefore, the reflection of (6,-5) across the line y=x is (-5,6).
To dilate a vector by a scale of -1.5, we multiply the vector by -1.5. Therefore, the resulting vector is (-5,6) multiplied by -1.5, which gives us:
(-5,6) * (-1.5) = (7.5, -9)
So the final result after the reflection and dilation is (7.5, -9).
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Please can someone help me
The vector v can be decomposed into v₁ = -2i - 2j and v₂ = -6i + 6j.
What is the decomposition of the vectors?The decomposition of the vectors is calculated as follows;
v₁ = (v · w / |w|²) w
v₂ = v - v₁
The dot product of v and w is calculated as;
v · w = (-8)(1) + (4)(1)
v · w = -4
The magnitude of w is calculated as;
|w| = √1² + 1²)
|w|= √2
|w|² = 2
The value of v₁ is calculated as;
v₁ = (-4 / 2) (i + j)
v₁ = -2i - 2j
The value of v₂ is calculated as follows;
v₂ = v - v₁
v₂ = (-8i + 4j) - (-2i - 2j)
v₂ = -6i + 6j
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Christo wants to buy a small wine farm worth R8 500 000. He plans to sell his current home for R3 400 000 which he will use as a deposit for the purchase of the farm. He secures a loan with a bank with a repayment period of 10 years and an interest rate of 9, 5% compounded monthly. Calculate his monthly repayments.
Christo's monthly repayments for a loan of R5,100,000 for 10 years at 9,5% interest compounded monthly is R65,992.75.
How is the monthly repayments determined?The monthly repayments can be determined using an online finance calculator as follows:
The monthly repayments show the periodic payments to settle the loan.
Wine Farm Price = R8,500,000
Down Payment = R3,400,000
Loan Term = 10 years
Interest Rate = 9.5%
Start Date = Apr. 2023
Monthly Pay: R65,992.75
Loan Amount = R5,100,000.00
Total of 120 Mortgage Payments = R7,919,130.52
Total Interest = R2,819,130.52
Mortgage Payoff Date = Apr. 2033
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Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon?
0.67
0.53
0.5
0.47
The experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon is 0.53. Therefore, option B is the correct answer.
The given sample space is {ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr}
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.
Here, total number of outcomes = 30
Number of favorable outcomes =16
Probability of an event 16/30
= 0.53
Therefore, option B is the correct answer.
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An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different banks. The terms of each loan are:
Offer 1: 2.99% annual simple interest, with a total account balance of $81,353.75 after a 34-month term
Offer 2: 1.5% annual interest compounded monthly for a 38-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest penny.
O$1,718.99
O $2,001.57
O $2,707.62
O $2,489.68
Answer: 2,001.57
Step-by-step explanation:
there ya go!
1/3 divided by 2/9 simplified?
Answer:3/2
Step-by-step explanation:
1/3 ÷ 2/9=
1/3 ×9/2=3/2
Answer:
3/2 u can also do 1 1/2 their equivalent fractions
Step-by-step explanation:
sorry about the handwriting :) not the best
ILL GIVE 20 POINTS !!!! PLSS HELP ASAP
Answer: 10/40 or 1/4
Step-by-step explanation:
Add up all the amount of rolls, so 10+6+4+8+6+6=40
then add the probability of rolling a 3 or 6 = 10
divide that quantity out of the whole
answer is 10/40 and simplified is 1/4
hope it helps
