A woman deposits $300 in a savings account that pays 6% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)?
The woman will withdraw $300 given 6% interest rate annually.
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:
r = 0.06/365 = 0.00016438356
The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:
I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999
The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:
300 + 0.017 = $300.02
Rounding to the nearest dollar, the woman will withdraw $300.
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find each unknown. Double a known fact.
9 x 4=
Answer: 36
Step-by-step explanation:
A local charity is selling seats to a baseball game. Seats cost $16 each, and snacks cost an additional $4
each. The charity needs to raise $160 to consider this event a success.
Use the graph to approximate how many snacks the charity must sell if 5 seats are sold.
Step-by-step explanation:
16$ per seat
*5 seats 16 * 5 = 80
80$ for 5 seats
160$ - $80 = 80$
The remaining money is 80 dollars which need to be spent on snacks:
4$ per snack
80$ / by 4$ = 20 snacks
Work ✔:
20 snacks = 80$
5 seats = 80$ Charity Goal = 160$
80$ + 80$ = 160$
Final answer:
The charity must sell 20 snacks to every five seats to reach the charity goal of 160$
Hope this Helps! :D
1. Gracie and her son Landon are celebrating spring with an egg hunt! Gracie has hidden eggs filled with candy
for Landon to find.
(a) Landon finds a total of 27 eggs. One third of the eggs have 4 pieces of candy, the rest have 2 pieces of
candy. How many pieces of candy did Landon get?
(b) Gracie offers him a deal: he can either have three pieces of candy now, or if he waits until after lunch he
can have one-seventh of his candy. Which way gets Landon the most candy?
Answer:
a is 72 total pieces of candy
b is more candy if he waits and gets one-seventh
Step-by-step explanation:
a. 9 eggs have 4 so 9x4=36
leaving 18 eggs with 2 so 18x2=36
36+36=72 total
b. 3 now or...
1/7 x 72 = 10.28
Answer:
b.72×1/7=10.28
I think he can wait untul after lunch time
Step-by-step explanation:
Hope this right.But if it's not,im so sorry...Have a nice day
Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm with a sample standard deviation of 1.9 cm. The heights of all bread loaves are assumed to be normally distributed. The baker is now interested in obtaining a 95% confidence interval for the true mean height of his loaves. What is the lower bound to this confidence interval? 2 cm (round to 2 decimal places) What is the upper bound to this confidence interval? cm (round to 2 decimal places) For the following situations, use RStudio to find the appropriate t-critical values that would be needed to construct a confidence interval. Round all critical values to the second decimal place. 1. n = 15, confidence level is 95%, x= 35 and s = 2.7, t-critical value- 2, n = 37, confidence level is 99%, x= 82 and s = 5.9 t-critical value- 2 3, n 1009, confidence level is 90%, x 0.9 and s-0.04 t- critical value = 2 2
The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm
To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.
The formula for a confidence interval for the population mean (μ) is:
Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))
For the first situation:
n = 15
Confidence level is 95% (which corresponds to an alpha level of 0.05)
x = 35 (sample mean)
s = 2.7 (sample standard deviation)
Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.
The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.
Plugging the values into the formula:
Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))
Calculating the confidence interval:
Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)
Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.
For the second situation:
n = 37
Confidence level is 99% (which corresponds to an alpha level of 0.01)
x = 82 (sample mean)
s = 5.9 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.
The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.
Plugging the values into the formula:
Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))
Calculating the confidence interval:
Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)
Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.
For the third situation:
n = 1009
Confidence level is 90% (which corresponds to an alpha level of 0.10)
x = 0.9 (sample mean)
s = 0.04 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.
The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.
Plugging the values into the formula:
Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))
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A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
A total of 3 ft falls over 3 days. On the first day, 1/6 of the total rain falls. On the second day, 7/12 of the total rain falls. How much rain falls each day in inches? Show your work. Please help.
Answer:
Day 1: 6 inches
Day 2: 21 inches
Day 3: 9 inches
Step-by-step explanation:
First, we need to convert the total rainfall from feet to inches. Since 1 foot is equal to 12 inches, 3 feet is equal to 36 inches.
On the first day, 1/6 of the total rainfall falls, so:
(1/6) * 36 = 6 inches
On the second day, 7/12 of the total rainfall falls, so:
(7/12) * 36 = 21 inches
To find the rainfall on the third day, we can subtract the rainfall on the first and second days from the total rainfall:
36 - 6 - 21 = 9 inches
Therefore, the amount of rainfall on each day, in inches, is:
Day 1: 6 inches
Day 2: 21 inches
Day 3: 9 inches
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.5447
b) 0.0228
c) 0.4325
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.
This means that \(\mu = 9.6, \sigma = 2.3\)
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So
X = 10
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{10 - 9.6}{2.3}\)
\(Z = 0.17\)
\(Z = 0.17\) has a p-value of 0.5675
X = 5
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{5 - 9.6}{2.3}\)
\(Z = -2\)
\(Z = -2\) has a p-value of 0.0228
0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.
1 - 0.5675 = 0.4325
0.4325 probability that a randomly received emergency call is of more than 10 minutes.
1/5x + 1/4 = 1/2(x+5) Answer Plz I Need It!
Answer:
x=-15/2
Step-by-step explanation:
Joshua is going to invest $1,000 and leave it in an account for 18 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Joshua to end up with $1,500 ?
The rate is of interest such that the initial investment of $1,000 becomes $1,500 in 18 years will be 2.25%.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $1,000
Time period T = 18 years
Interest rate = R %
Number of times interest applied per time period n = 12
Total investment = P[1 + R/n]^(nT)
1500 = 1000[1 + R/12]^(12 x 18)
1.5= (1 + R/12)²¹⁶
1.001878916 = 1 + R/12
R = 0.02256 = 2.25%
Hence "The rate is of interest such that the initial investment of $1,000 becomes $1,500 in 18 years will be 2.25%".
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A high school is running a campaign against the over-use of technology in teens. The committee running the campaign decides to look at the difference in social media usage between teens and adults. They take a random sample of 200 teens in their city (Group 1) and find that 85% of them use social media, and then take another random sample of 180 adults in their city (Group 2) and find that 55% of them use social media. Find a 90% confidence interval for the difference in proportions.
Answer:
0.226, 0.374
Step-by-step explanation:
A high school is running a campaign against the over-use of technology in teens. The committee running the campaign decides to look at the difference in social media usage between teens and adults. and then Find a 90% confidence interval for the difference in proportions.
The formula for confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
From the question
We have two groups.
Group 1
They take a random sample of 200 teens in their city (Group 1) and find that 85% of them use social media,
p1 = x/n1
n1 = 200
x1 = 85% × 200 = 170
p1 = 170/200
p1 = 0.85
Group 2
Take another random sample of 180 adults in their city (Group 2) and find that 55% of them use social media.
p2 = x/n1
n2= 180
x2 = 55% × 180 = 99
p2 = 99/180
p2 = 0.55
z = z score for 90% Confidence Interval = 1.645
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
= 0.85 - 0.55 ± 1.645 √0.85(1 - 0.85)/200 + 0.55(1 - 0.55)/180
= 0.85 - 0.55 ± 1.645 √0.85(0.15)/200 + 0.55(0.45)/180
= 0.30 ± 1.645 × √0.0020125
= 0.30 ± 1.645 × 0.0448608961
= 0.30 ± 0.0737961741
Hence
= 0.30 - 0.0737961741
= 0.2262038259
= 0.30 + 0.0737961741
= 0.3737961741
Therefore, 90% confidence interval for the difference in proportions is (0.226, 0.374
A bank offers two checking account plans. Plan A has a base service charge of $9.00 per month plus 7 cents per check. Plan B charges a base service charge for $1.00 per month plus 27 cents per check. For what number of checks per month will plan A be better than plan B?How would I write that in interval notation?
Answer:
• The number of checks, c is greater than 40.
,• (40, ∞)
Explanation:
Let the number of checks per month = c
Plan A
• Base service charge = $9.00 per month.
,• Charge per check =7 cents = $0.07
The total cost for plan A is: 9+0.07c
Plan B
• Base service charge = $1.00 per month.
,• Charge per check =27 cents = $0.27
The total cost for plan B is: 1+0.27c
For plan A to be better than plan B, the total cost for plan A must be less than the total cost for plan B. That is:
\(9+0.07c<1+0.27c\)The inequality is solved for c.
\(\begin{gathered} 9-1<0.27c-0.07c \\ 8<0.2c \\ \text{Divide both sides by 0.2} \\ \frac{8}{0.2}<\frac{0.2c}{0.2} \\ 4040 \end{gathered}\)Plan A will be better than Plan B whenever the number of checks is greater than 40.
This can be written in the interval notation as:
\((40,\infty)\)If A(0, 4), B(5, y), and AB = 13. What is y?
The required value of y for the given segment AB is given as y = 16, -8.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
here,
A(0, 4), B(5, y), and AB = 13.
Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]
Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12
y = 16, -8
Thus, the required value of y for the given segment AB is given as y = 16, -8.
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Draw the net and calculate the surface area .
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
One angle of a right triangle measures 51°. What is the measure of the other acute angle, in degrees?
Answer:
39 degree
Step-by-step explanation:
180-90-51=39
The conical sells for $2.50 and the cylindrical container sells for $3. What is true about the popcorn containers?
Answer:you got this you dont need this site but if you do ask me
Step-by-step explanation:
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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A movie theater charges $ 6.00 for adults and $3.00 for senior citizens. On a day when people paid for admission, the total receipts were $1293. How many who paid were adults? How many were seniors?
1. Using a system of equations, the number of adults who paid was 101.
2. Using a system of equations, the number of seniors who paid was 229.
What is a system of equations?A system of equations involves the use of more than one equation to solve an equation problem simultaneously.
A system of equations is also known as simultaneous equations.
Charge per adult = $6
Charge per senior = $3
The total receipts = $1,293
The number of movie-goers who paid = 330
Let adults = x
Let seniors = y
6x + 3y = 1,293 ... Equation 1
x + y = 330 ... Equation 2
x = 330 - y ... Equation 3
In Equation 1:
6(330 - y) + 3y = 1,293
1,980 - 6y + 3y = 1,293
-6y + 3y = 1,293 - 1,980
-3y = -687
y = 229
In Equation 3:
x = 330 - y
x = 330 - 229
x = 101
Check:
In Equation 1:
6x + 3y = 1,293
6(101) + 3(229) = 1,293
606 + 687 = 1,293
1,293 = 1,293
Thus, using a system of equations, adults who paid were 101 and seniors were 229.
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Question Completion:On a day when 330 people paid for admission, the total receipts were $1293.
Given the following data sample, how confident can we be that the mean is greater than 40? 64 70 20 58 13 74 84 47 17 2. You are given the following sample of annual returns for portfolio manager: If you believe that the distribution of returns has been stable over time and will continue to be stable over time; how confident should you be that the portfolio manager will continue to produce positive returns? -7% 7% 19% 23 % -18 % -12% 49% 34% ~6% -20% 3 . You are presented with an investment strategy with a mean return of 20% and standard deviation of 10%_ What is the probability of a negative return if the returns are normally distributed? What if the distribution is symmetrical, but otherwise unknown?'
The probability of a negative return if the returns are normally distributed, we can use the mean and standard deviation of the returns and If the distribution is symmetrical but otherwise unknown, it may be more difficult to estimate the probability of a negative return without more information about the shape of the distribution.
To determine how confident we can be that the mean of the given data sample is greater than 40, we would need to perform a statistical test such as a t-test or a z-test to compare the sample mean to the value of 40.
We would need to know the sample size, standard deviation, and any other relevant information about the data to calculate the appropriate test statistic and determine the p-value, which would tell us the probability of observing a sample mean as extreme as the one we obtained if the true population mean was actually 40.
To determine how confident we should be that the portfolio manager will continue to produce positive returns, we would need to analyze the distribution of returns and determine whether it is skewed or symmetrical and whether it follows a normal distribution or a different distribution. If the distribution is skewed or non-normal, it may be more difficult to estimate the probability of positive returns. However, if the distribution is symmetrical and follows a normal distribution, we can use the mean and standard deviation of the returns to calculate the probability of a positive return using the normal distribution.
If the returns of the investment strategy are normally distributed, we can use the mean and standard deviation of the returns to calculate the probability of a negative return using the normal distribution. If the distribution is symmetrical but otherwise unknown, it may be more difficult to estimate the probability of a negative return without more information about the shape of the distribution.
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The question is -
Given the following data sample, how confident can we be that the mean is greater than 40? 64 70 20 58 13 74 84 47 17 2. You are given the following sample of annual returns for the portfolio manager: If you believe that the distribution of returns has been stable over time and will continue to be stable over time; how confident should you be that the portfolio manager will continue to produce positive returns? -7% 7% 19% 23 % -18 % -12% 49% 34% ~6% -20% 3. You are presented with an investment strategy with a mean return of 20% and a standard deviation of 10%_ What is the probability of a negative return if the returns are normally distributed? What if the distribution is symmetrical but otherwise unknown?'
Solve 2^x-2=8^4 but not solving for x
Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.
To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.
First, let's simplify the equation:
2^x - 2 = 8^4
We know that 8 can be expressed as 2^3, so we can rewrite the equation as:
2^x - 2 = (2^3)^4
Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:
2^x - 2 = 2^(34)
Simplifying the right side of the equation:
2^x - 2 = 2^12
Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:
x = 12
Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.
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translate then solve:five times the difference of twice and number and three decreased by the sum of the number and 8 equals 13
Answer: x = 4
Step-by-step explanation:
Translating the problem into mathematical terms:
Let's call the number x. Then the problem can be written as:
5 * (2x - 3) - (x + 8) = 13
Expanding the left side of the equation:
5 * 2x - 5 * 3 - x - 8 = 13
Simplifying the left side of the equation:
10x - 23 - x - 8 = 13
Combining like terms:
9x - 31 = 13
Adding 31 to both sides of the equation:
9x = 44
Dividing both sides of the equation by 9:
x = 4.88888...
Since x has to be a whole number, we round down to the nearest whole number:
x = 4
Therefore, the number that satisfies the equation is 4.
Please help needed!!
A point= zero-dimensional object designates a particular place on a plane. Moreover, a little dot is used to symbolize it.
What is a geometric figure?A geometric figure is a collection of lines, planes, or points that together form the shapes of various three-dimensional things.
A geometric figure is referred to in geometry using the terms and definitions below:
A point, or zero-dimensional object, designates a particular place on a plane. Moreover, a little dot is used to symbolize it. ⇒Image 4.A line is a one-dimensional shape that stretches in two (2) directions without having an end. (Image 5)Line segments are the discrete portions of a line that connect any two (2) points on the line. (Image 1.)A ray is a half-line that begins at one place and extends in one direction indefinitely (forever) (Image 3).A plane is a two-dimensional surface that never ends( Image 2.).To know more about Geometry visit:
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Please help!! Will give thanks
Question is in photo!
Answer:
linear
Step-by-step explanation:
its increasing at a steady rate each year. hope it helps!!!!
A decorative vase is on sale from $80 to $50. What is the
percent change of the price of the vase. Be sure to indicate
if it was a decrease or increase. Show the formula you use to
solve. Round to a whole number.
Since the result is negative, we can say that the price of the vase decreased by 37.5%. Rounding to a whole number, the percent change is 38% (since a 37.5% decrease is approximately equal to a 38% decrease).
What is percent?Percent (often symbolized as "%") is a way of expressing a fraction or a portion of something in terms of hundredths. It is used to describe the relationship between a part and a whole, with the whole being represented by 100%. Percentages are commonly used in many areas of life, such as finance, business, and statistics. They can be used to describe changes in values over time, to compare different quantities or amounts, or to express probabilities or frequencies.
Here,
The percent change in the price of the vase can be calculated using the formula:
percent change = (new price - old price) / old price x 100%
In this case, the old price of the vase was $80 and the new price is $50. Substituting these values into the formula, we get:
percent change = ($50 - $80) / $80 x 100%
percent change = -0.375 x 100%
percent change = -37.5%
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PLEASE HELP BEFORE 4 PM!!!
1. 641 divided by 43
2. 4684 divided by 27
3. 6455 divided by 64
Answer:
1. Its about 14.90697674418605. I’m not sure if u want it rounded up if u want it rounded up to the nearest whole it would be 15 if I wanted it rounded up to the nearest tenth then it would be 14.9
2. It’s about 173.4814814814815. I wasn’t sure if I wanted this one rounded up too. Rounded up to the nearest whole it would be 173 and rounded up to the nearest tenth it would be 173.5
3. It’s about 100.859375. I wasn’t sure on this one too. Rounded up to the nearest whole would be 101 and rounded up to the nearest tenth it would be 100.9
Step-by-step explanation:
Find cos 0 , help asap
D.
Step-by-step explanation:
because cos0 = b/h
so cos0 = 8/15
Principal amount: $1,000
Interest rate: 10%
Time: 12 months
The Simple Interest on Principal amount: $1,000 is $100.
What is Simple Interest?Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.
Given:
Principal amount: $1,000
Interest rate: 10%
Time: 12 months
So, the Simple Interest
= P x R x T/100
= 1000 x 10 x 1 / 100
= 10000/100
= $100
and, Amount = P + I
Amount = $1100
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Math question
The average low temperature in City A in December is 4 C. In March it is
12 C lower. What is the average low temperature in City A in March?
Find the unit cost (i.e. dollars per unit). Round the answer to 3 decimal places when necessary. A package of 3 AAA batteries costs $3.36.
Place √31 in the appropriate place on the number line. Round to tenths
Answer: To place √31 on the number line, we first need to find its approximate value.
√31 is between 5 and 6 since 5²=25 and 6²=36. To find a more precise value, we can use a calculator or estimate using long division.
Using a calculator, we get:
√31 ≈ 5.56776436
Rounding to tenths, we get:
√31 ≈ 5.6
To place 5.6 on the number line, we can mark the point between 5.5 and 5.7.
Here's a rough sketch of what it might look like:
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Step-by-step explanation: